"Frederick Williams" <firstname.lastname@example.org> 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 not-CH.
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.