Re: Implementable Set Theory and Consistency of ZFC

On Tue, 30 Oct 2007 13:36:30 +0100, Han de Bruijn
<Han.deBruijn@xxxxxxxxxxxxxx> wrote:

David C. Ullrich wrote:

On Mon, 29 Oct 2007 15:22:53 +0100, Han de Bruijn
<Han.deBruijn@xxxxxxxxxxxxxx> wrote:

David C. Ullrich wrote:

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

I have shown that, once accepted the truth of Empty set, Extensionality,
Pairing and Union, it follows that Substitution, Specification, Choice,
Foundation and Power Set are just true. Nothing more, nothing less.

Nope. Simply not so, regardless of how many times you repeat the
claim.

Hint: Accepting the truth of those four axioms is not the same thing
as restricting to your particular model. Those axioms have many
_other_ models.

My "particular model" is the general way to do implementable set theory.

I'll keep saying this until someone stands up who convinces me that I'm
wrong. Up to now, only _one_ debater has come up with a sensible example
of an_other_ model. Which I'm studying right now. But he is not Ullrich.
The latter person keeps faire blah blah about oh so many _other_ models
without showing me one, just _one_.

If you knew anything about logic you'd know that any consistent
theory with an infinite model has more than one model.

(Yes, your model is infinite - even though each set in the
model is a finite set, there are infinitely many sets.)

Han de Bruijn


************************

David C. Ullrich
.

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