[FOM] Arithmetical soundness of ZFC
T.Forster at dpmms.cam.ac.uk
Sun May 24 04:14:08 EDT 2009
Isn't this easy? Don't most (if not all) ZF-istes believe that (i) ZF(C)
is not only consistent but sound *as a theory of (wellfounded) sets*?
And (ii) isn't the obvious interpretation of arithmetic into ZF (natural
numbners are cardinals of finite sets) sufficiently faithful to ensure
that ZFC's theory of natural numbers is sound too?
I know this is only a sketch, but surely something like this must be
what is going on at the back of the mind of anyone who thinks ZF(C) is
arithmetically sound. It might be worth thinking which of (i) and (ii)
DPMMS ph: +44-1223-337981;
UEA ph: +44-1603-592719
mobile in UK +44-7887-701-562;
mobile in US: +1-412-818-1316;
mobile in NZ +64-210580093.
More information about the FOM