Re: Implementable Set Theory and Consistency of ZFC

Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:

Jesse F. Hughes wrote:

But whatever it means, since a model of ZFC is also a model of
ZFC - Infinity, you seem to be claiming that you can build an infinite
set using only the first four axioms.

But the reverse is not true: a model of (ZFC - Infinity) is not a model
of ZFC(Infinity included). So I'm building only (ZFC - Infinity), with
those first four axioms: extensionality, empty set, pairing, union. All
finite sets can be build with these 4 axioms (but there are infinitely
many of these finite sets, like with the naturals).

In other words, you are *not* speaking about every model of
ZFC - Infinity, despite what you claimed.

And just as I suggested.

--
Jesse F. Hughes
"Maybe I screwed up on one of my assumptions [...]. Otherwise, um,
it's very easy to factor, and things are about to get really, really
weird." -- James S. Harris
.

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