Re: Implementable Set Theory and Consistency of ZFC

MoeBlee wrote:

On Oct 31, 1:59 am, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:

Jesse F. Hughes wrote:

I will say it once more. I am typing this slowly, since I don't want
you to miss anything I say. If you have a proof in a theory
consisting of axioms (1)-(4), it is also a proof in the theory
consisting of axioms (1)-(4)+(X).

How do you "know" that? Has the Pope told you, by dogma, that it is so?

No, you royal ignoramus, it's PROVEN as a basic property of the
deductive system. It's the property of monotonicity of deduction. And
we PROVE it.

Yeah, yeah. Then why are (5-9) required in ZFC, once Infinity has become
an axiom of it? Why is e.g. Choice provable in (ZFC-Infinity) and not in
common ZFC?

Han de Bruijn

.

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