Virgil
Posts:
4,479
Registered:
1/6/11
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Re: Finitely definable reals.
Posted:
Jan 17, 2013 5:52 PM
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In article
<a51cc441-9f02-4092-b11b-a5ecc62abf45@g6g2000vbk.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 16 Jan., 08:32, Virgil <vir...@ligriv.com> wrote:
>
> >
> > But it also shows that no finite set is maximal in ZF or ZFC, the
> > axiom of infinity requires that for every finite set there is set
> > with more members.
I.e., in ZF, for every set S
1. S is not a member of itself, and
2. S is a proper subset of Union(S, {S})
>
> But the powerset of all powersets of N, U = PPP...PPP(N) such that
> P(U) = U, is not required?
However much it may be required in WMytheology, it is not at all
required in ZF or ZFC, and is, in fact, prohibited.
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