[FOM] Arithmetical soundness of ZFC
joeshipman@aol.com
joeshipman at aol.com
Sun May 24 01:47:47 EDT 2009
If ZFC proved "ZFC is inconsistent" (which is weaker than proving 1=0
because ZFC could still be consistent but omega-inconsistent) then that
could be converted into a proof that ZFC is not sound.
We would expect a sound theory to be omega-consistent with respect to
arithmetical statements.
I cannot think of any other possible way in which we could come to
believe in the non-arithmetical soundness of ZFC than a proof that ZFC
is omega-inconsistent.
-- JS
-----Original Message-----
From: Harvey Friedman <friedman at math.ohio-state.edu>
BUT WHAT WOULD A PROOF OF THE NON ARITHMETICAL SOUNDNESS OF ZFC LOOK
LIKE?
More vaguely,
WHAT WOULD EVIDENCE OF THE NON ARITHMETICAL SOUNDNESS OF ZFC LOOK LIKE?
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