Re: Implementable Set Theory and Consistency of ZFC

On Oct 31, 6:22 am, "Jesse F. Hughes" <je...@xxxxxxxxxxxxx> wrote:

Here's my statement of ~Infinity:

Every set has a finite number of members. In other words, every set
can be put in one-to-one correspondence with some set {0,1,...,n}.

Or 1-1 with the empty set.

But I don't know how to derive that as an equivalent of the axiom of
infinity, where the axiom of infinity is Ex(0ex & Anex nu{n) e x).

I see that, in Z-I, "every set is 1-1 with a natural number" entails
the negation of the axiom of infinity. But how, in Z-I, do you derive
"every set is 1-1 with a natural number" from the negation of the
axiom of infinity?

MoeBlee

.

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