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Topic: question on set theory
Replies: 4   Last Post: Jan 4, 2013 2:17 AM

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matmzc%hofstra.edu@gtempaccount.com

Posts: 3
Registered: 1/2/13
Re: question on set theory
Posted: Jan 3, 2013 2:22 AM
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On Wednesday, January 2, 2013 3:30:01 PM UTC-5, Dan Luecking wrote:
> On Wed, 2 Jan 2013 17:37:20 +0000 (GMT),
>


Apologies everyone. I posted the question late at night and wrote the proposition backwards. I meant to say consider

Prop: If X < Y then P(X) < P(Y)

Can that be proved in ZFC? If not is it perhaps equivalent to generalized continuum hypothesis? It is easy to show in ZF with or without choice that that X < Y implies P(X)<=P(Y). But can it possibly be the case that X < Y but P(X)=P(Y)?

Mike





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