Re: Implementable Set Theory and Consistency of ZFC

In article <9c2c6$471dd9a2$82a1e228$25199@xxxxxxxxxxxxxxxx>,
Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> wrote:

Jesse F. Hughes wrote:

Why not just tell me what you meant when you said that your claim
applied to "any implementation" if not "any model of these eight
axioms"?

Don't know what kind of silly word game you are playing with me this
time, but what I mean is a "model" of the following except "X":

1. Extensionality 5. Specification X. Infinity
2. Empty set 6. Substitution
3. Pairing 7. Power Set
4. Union 8. Foundation
9. Choice

And, as I've said, in this "model", only (1-4) are necessary as axioms,
because (5-9) appear as theorems. And (X) is not part of the "model".


And where does one find formal proofs of (5-9) based only on axioms
(1-4)?
.

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