
Re: unable to prove?
Posted:
Aug 27, 2012 6:07 PM


"Frederick Williams" <freddywilliams@btinternet.com> wrote in message news:503BDB35.E2CE8638@btinternet.com... > dilettante wrote: >> >> [...] I suppose it isn't known whether positing the >> existence of the power set of the reals leads to a contradiction. Surely >> also taking the existence of this set as an axiom doesn't do anything to >> resolve CH (of course, as far as anyone knows  if it leads to a >> contradiction it resolves everything, in a sense)? (Yes, that's a >> question) > > It is known that if the axioms of set theory are consistent then they > remain so with the addition of either CH (or even GCH) or notCH.
But what do the axioms of set theory have to say about the power set of the reals? Is that a set under the axioms, not a set, or are the axioms agnostic on the matter? > >  > The animated figures stand > Adorning every public street > And seem to breathe in stone, or > Move their marble feet.

