Re: Largest Set in ZFC?

<SNIP>

> The definition is:

> {S} = {S S}

> and, of course {S S} we get from pairing..

Thanks. I was curious how that worked.
If S is a set then pairing says {S,S} is a set
and extensionality says {S,S} = {S}.


*** I had never even noticed the issue, interesting.


It seems AoI is deliberately vague about what
sets are members of X. Why is that?

I don't know the motivation of the actual people who wrote it, but the
reason I personally would give is this: We don't NEED to be any more
specific, since separation does the rest of the job for us to get to
the specific set w that we want.

*** I know much less about this topic than you do, but it seems there is a more fundamental reason for the vagueness of the definition of X. If anybody could produce a specific such X, then they would have a model of ZF (a collection of sets that satisfy ZF). This would prove the consistency of ZF. AFAIK, there is no theoretical reason why such a set X could not be described, but none ever has, and its seems pretty obvious that none ever will. Hence the requirement to vague it up a bit.


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