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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: unable to prove?
Replies: 28   Last Post: Sep 18, 2012 3:54 PM

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Frederick Williams

Posts: 2,166
Registered: 10/4/10
Re: unable to prove?
Posted: Aug 27, 2012 4:40 PM
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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.

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