Re: Implementable Set Theory and Consistency of ZFC

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.

This is _incredibly_ stupid.

Yes. I agree with you that _this_ is incredibly stupid.

You really have no conception of
what it means to say A follows from B.

I _have_ such a conception, but obviously they who conceived set theory,
as a vague mixture of finite and infinite sets, didn't have such a clear
conception.

Han de Bruijn

.

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