Re: Implementable Set Theory and Consistency of ZFC

On Oct 23, 4:23 am, Han de Bruijn <Han.deBru...@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".

Why do you keep putting 'model' in scare quotes? If you have a
different definition of 'model' then you should state it and, I'd
suggest, use a different word, say, 'hmodel'. But if your definition
is the ordinary one in mathematical logic, then there's no need for
scare quotes.

So, when you say, "And [the axiom of infinity] is not part of the
"model"", that makes no apparent sense. Ordinarily, axioms are not
things that are "part of a model".

You seem not to understand the notion of a model. What textbook in
mathematical logic do you usually refer to?

MoeBlee


.

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