Re: Implementable Set Theory and Consistency of ZFC

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

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.

Weird. How come no one else can recognize that you've done that?

Also, if you *had* done that, then axioms (1)-(4) + (9) would be
sufficient for ZFC. Don't you find it a touch odd that no one else
has noticed this fascinating fact?

You *do* know that if (1)-(4) prove (5)-(8), then so do (1)-(4) + (9),
right?

--
"Is that possible? Could it be that easy? No way. [...] There must be
a mistake. Right?

"But I am the top mathematician in the world." -- James S. Harris
.

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