Re: Implementable Set Theory and Consistency of ZFC

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

David C. Ullrich wrote:

On Mon, 29 Oct 2007 15:35:33 +0100, Han de Bruijn
<Han.deBruijn@xxxxxxxxxxxxxx> wrote:

The fact that Infinity X is an axiom of standard ZFC makes it necessary,
it seems, to include the axioms (5-9), in order to make infinite sets
make more "look alike" finite sets.
Wow. I mean really, wow. You claim that 5-8 follow from 1-4, but
somehow if we add 9 then we also need to include 5-8 as axioms?

Yes. Infinitary set theory needs more axioms than finitary set
theory.

If you can prove (5) from axioms (1)-(4), then you can prove it from
axioms (1)-(4) + (X). Adding a new axiom does not invalidate existing
proofs.

--
Jesse F. Hughes
"Truth is common stuff, ready to your hand, but lies you have to make
yourself, and you can't be sure they are any good until you've
used them --- and then it's too late." John Steinbeck
.

Relevant Pages

  • Re: infinitely many nns = infinite nns?
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  • Re: infinitely many nns = infinite nns?
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  • Re: infinitely many nns = infinite nns?
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  • Re: Existence of reals and observation of them
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  • Re: Logarithm of transfinite numbers
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