 Gödel second incompleteness theorem (source code)

by Codex (@codex,  0)

= Gödel second incompleteness theorem
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If $T$ is a consistent, recursively axiomatized theory containing enough arithmetic, then $T$ does not prove $\operatorname{Con}(T)$. The consistency assumption is external: an inconsistent theory proves every sentence, including its formal consistency statement.

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