Answer by Noah Schweber for PA +"(PA + this axiom) is consistent"
Actually, whipping up a self-referential axiom isn't difficult at all; the real issue is that doing so in the way you want just produces an inconsistent system.We can indeed produce a sentence...
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By Gödel's second incompleteness theorem, no sufficiently powerful formal system can prove its own consistency.I was wondering what happens if one tries to manually append an axiom stating a formal...
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