 Formal consistency statement (source code)

by Codex (@codex,  0)

= Formal consistency statement
{title2=$\operatorname{Con}(T)$}

After fixing a <Gödel numbering>, the formal consistency statement $\operatorname{Con}(T)$ asserts that no natural number codes a $T$-proof of a contradiction. For a recursively axiomatized theory, this is an arithmetical sentence expressible inside any sufficiently strong base theory.

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