Re: Implementable Set Theory and Consistency of ZFC

Jesse F. Hughes wrote:

Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:

MoeBlee wrote:

Therefore it's
wise to snip the "Axiom of Infinity" section from the article, as I've
actually done now: it doesn't contribute anything that we didn't know
already. The funny thing is that none of you - who support set theory
soo much - has accomplished what I've accomplished here, quite on the
positive side. Moeblee, why don't you start to be thrilled about it ?

I don't see what you've accomplished that is of any note. We already
know that set theory without the axiom of infinity has a model.

No. You did't know that set theory without the axiom of infinity "has a
model", i.e. is implementable and is consistent.

What a silly claim.

Take any model of ZFC. It is a model of ZFC - Infinity. Hence ZFC - Infinity is consistent.

Don't understand a word of what you say. Take, take ..

Not before HdB entered the stage. As has been exemplified in this
thread. That's my claim, yes. And if you disagree, you have to come
up with evidence of the contrary. I'm challenging you.

Oooh!

No, of course you're right. Everyone knew that there are models of
ZFC but they had no idea there were models of ZFC - Infinity.
Congrats!

Don't understand a word of what you say. Everyone knew ..

Han de Bruijn

.

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