[FOM] The Minimal Model of ZF

joeshipman@aol.com joeshipman at aol.com
Wed Jan 2 22:15:42 EST 2008

-----Original Message-----
From: Ilya Tsindlekht <eilya497 at 013.net>
>For each element of M M has a formula naming it. It just doesn't have
>the function which maps each such formula to the defined element.

Yes, but what are we to make of those formulas when M is a proper 
class? Do they still pick out (countably infinitely many) unique 
elements of M, just not all the elements of M? Can we define the first 
ordinal which is not picked out?

There is a subtle mistake in the previous paragraph; but I am trying to 
take seriously the axiom V=M by the paradoxical trick of assuming M is 
a set, since then it satisfies V=M and its theory Th(M) is a complete 
theory extending V=M; this tells us some additional facts about Th(M), 
for example that it contains Con(ZF) (which is not an official logical 
consequence of ZF+V=M).

-- JS
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