[FOM] Arithmetical soundness of ZFC

[joeshipman@aol.com]

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?