Re: Countable models of ZFC

On Sep 21, 9:53 am, "LordBeotian" <pokips...@xxxxxxxx> wrote:
|Are there explicit examples of countable models for ZFC?

It might be worth pointing out that the completeness
theorem can be proved in a way that provides
explicit examples of models of an arbitrary countable
consistent theory. One proof in effect constructs a
binary tree which if finite yields a proof of the
inconsistency of the theory, and where any infinite
branch yields a model of the theory.

We can pick an explicit example of an infinite branch,
for example the "leftmost" infinite branch, which is
arithmetically definable. In the case of ZFC, this gives
us a somewhat "eccentric" model, however, due to
the arithmetic definability of the model.

Keith Ramsay

.

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