Re: Implementable Set Theory and Consistency of ZFC

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).

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.
The ninth axiom of ZFC, Infinity, is _not_ implementable.

Better?

You're still wasting a lot of paper to state that no infinite set
exists under the assumption that all sets are finite.

I've simply deleted now the last section, in:

http://hdebruijn.soo.dto.tudelft.nl/jaar2007/set_theory.pdf

Don't you see that people had a *reason* to include Infinity
as otherwise set theory had an useless simple model?

Personally, I don't find such more humble kind of set theory "useless".

Han de Bruijn

.

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