Re: Implementable Set Theory and Consistency of ZFC

On 18 okt, 19:52, "Jesse F. Hughes" <je...@xxxxxxxxxxxxx> wrote:
Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> writes:

hagman wrote:

This is still not correct as the Axiom of Infinity is an axiom of ZFC
and does not hold in your model (which is thus a model of ZFC-
Infinity, in fact one of ZFC-Infinity+~Infinity).

No. The latest version is about (ZFC-Infinity).
I've mentioned (+~Infinity) nowhere in the article.
Infinity is not denied, it's simply outside the scope of our article.

With help of a bijection, which was basically discovered by Alexander
Abian, a "simple model", or rather an _Implementation_ of Set Theory in
memory of common digital computers, has been conceived, in theory as
well as in practice. With the implementation it can be proved that eight
out of the nine axioms of ZFC are consistent, and that only the first
four axioms are necessary for a constructive build of all sets.

It's not clear to me what the last claim means, but regardless, it
must mean something about "all sets" in this particular model of
ZFC - Infinity and not all sets of ZFC.

No. It's about all sets in (ZFC - Infinity). And the "particular
model"
is any implementation, is anything applicable.

Han de Bruijn

.

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