Re: Implementable Set Theory and Consistency of ZFC

Jesse F. Hughes wrote:

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

David C. Ullrich wrote:

Saying he's wrong does not prove that he is. Your "proof" that 5-8
follow from 1-4 is simply not a correct proof - that's a fact,
independent of anything anyone may have said here.

Yes, you've declared that repeadedly, by _dogma_. Are you the Pope of
Mathematics or what? Or is it true that I'm not allowed to enter the
Sacred Rites of you and your companions?

No, you can prove him wrong. Using only the axioms (1)-(4) and any
standard first order logic, give a derivation of (5)-(8). That's how
you prove what you've claimed.

This is *not* what you've done. Instead, you've given a particular
model of (1)-(4) and shown that (5)-(8) are true in that model. But
that does not show that (5)-(8) are theorems of (1)-(4).

No. There is not _one_ model in the first place. There are at least four
of them: integer array, bitmap, character string, natural. Computational
Set Theory is about sets that can be computed, represented in a machine,
it's not "just a model" of a far more superior Theory of Sets. Bringing
set theory back to earth is what I want. And I've succeeded a great deal
in doing so. (It has been a surprise to me that nine out of the ten ZFC
axioms still stand and have not collapsed with demanding computability.)

Claiming that Ullrich is being dogmatic when he has repeatedly
explained *why* you haven't proved what you claim is a bit sad,
frankly. But not surprising, given that you've also insulted me due
to my nationality. No sense in actually addressing what Ullrich has
said nor in answering the questions I've asked, huh?

Han de Bruijn

.

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