By Tarski's Theorem, it's complement, the set of true statements in formal arithmetic, is not recursively enumerable. But the set of untrue statements might be. Is it?
2026-03-26 19:11:53.1774552313
Is the set of untrue statements recursively enumerable?
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If there were an algorithm to enumerate the false statements, just run it, and every time it produces a statement of the form "Not $S$", output $S$. That would enumerate the true statements.