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

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dilettante

Posts: 141
Registered: 5/15/12
Re: unable to prove?
Posted: Aug 27, 2012 6:07 PM
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"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 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.





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