On 10/30/2014 10:24 AM, Bruno Marchal wrote:

On 30 Oct 2014, at 00:12, LizR wrote:

you can delete your posts (I think?)

That is not so easy when a post has been already sent, I think, unless quantum delayed erasing perhaps (grin), but as zibbsay observes, I was not so much quibbling when saying that modern set theories does provide a span of infinities. With ZF, above ZF + "kappa exists" (kappa a large cardinal), the model of ZF becomes citizen of a set theory extension. You get the same of course with PA + "PA is consistent", somehow, and the arithmetical is known *inexhaustible*, like Turing studied for its PhD with Church, and is well described in Torkel Fraenkel book "The inexhaustible".

Torkel Franzen.

Brent

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