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)?