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

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Michael Stemper

Posts: 671
Registered: 6/26/08
Re: unable to prove?
Posted: Aug 28, 2012 9:22 AM
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In article <k1gr3b$hjb$>, "dilettante" <> writes:
>"Frederick Williams" <> wrote in message
>> 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?

One of the axioms of ZF is the Power Set Axiom, which can be loosely stated
as: if A is a set, P(A) is a set. So your question may be reduced to "are
the reals a set under the axioms of ZF?"

(If you were referring to other axioms than ZF, please ignore this post.)

Michael F. Stemper
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