Re: consistency of Zermelo set theory



Fjodor wrote:

Also consider: What could you conclude from the (possible) fact that a
theory proves its own consistency, as any inconsistent theory proves
everything (including its own consistency)?

Might as well remark that we can't conclude anything about the
consistency of a theory from the mere fact that it proves its
own inconsistency.

E.g., the theory PA + ~con(PA) is consistent if PA is.

--
hz
"Mathematics is best done without axioms."
-- Wolfgang Mückenheim corrects Euclid --
.

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