Michael Beeson's Research

The posted input files are now all mechanically generated from a master list of theorems.

The times shown in the following table are not the times required to find the proof, but rather the maximum time allocated to Otter to find the proof. The time is shown only when it had to be longer than the default, which was often 20 seconds when hints were used and 120 seconds when hints were not used.

For more information about our methodology see the top page of this project.

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Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

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error in get_chapter()
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Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

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Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

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Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

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Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

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Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Input File	Proof	Length	Strategy	Seconds	Commentary

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