Re: Implementable Set Theory and Consistency of ZFC

On Mon, 29 Oct 2007 09:50:18 +0100, Han de Bruijn
<Han.deBruijn@xxxxxxxxxxxxxx> wrote:

Jesse F. Hughes wrote:

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

Jesse F. Hughes wrote:

Even assuming that there are four models rather than one, so what?
The point is that you have *not* given a proof of (5)-(8) using only
axioms (1)-(4). Thus, you have not done what you said.
Even if you show that there are seven models for (1)-(4) in which
(5)-(8) are also true, you haven't done what you said. Even if you
show there are *infinitely* many models satisfying this condition, you
haven't done what you said. So, perhaps you should either do what
you said or change your claim.

No. Because _nothing_ sensible ever counts as a proof in your conception
of mathematics.

Quite wrong. I've told you what counts as a proof of the claim that
(5)-(8) are theorems of (1)-(4). Namely, a proof of each of (5)-(8)
using only (1)-(4) as axioms.

What is so controversial about that?

Nothing. I've done just _that_ in my article.

No, you haven't done that. You show that 5-8 are
true in a certain model.

Let those who can not keep up do not halt the parade ..

Uh huh.

Han de Bruijn


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David C. Ullrich
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