Virgil
Posts:
7,010
Registered:
1/6/11


Re: Finitely definable reals.
Posted:
Jan 17, 2013 5:52 PM


In article <a51cc4419f024092b11ba5ecc62abf45@g6g2000vbk.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.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. 

