Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.

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

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Herman Rubin

Posts: 386
Registered: 2/4/10
Re: question on set theory
Posted: Jan 2, 2013 2:15 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 2013-01-02, matmzc%hofstra.edu@gtempaccount.com
<matmzc%hofstra.edu@gtempaccount.com> wrote: > Happy New Year everybody!

> For a set X I will write X < Y to indicate that the cardinality
of X is strictly smaller than the cardinality of Y. Let me write P(X)
for the power set of X. Consider the proposition:

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

> Is it possible to prove this in ZFC (without continuum hypothesis)?
If not is it perhaps the case that the Prop is equivalent to generalized
continuum hypothesis? It is trivial to show that generalized continuum
hypothesis implies the proposition, but what about the other direction?

Yes, and rather easily. With C, we have the trichotomy,
either X < Y, X ~ Y, or X > Y. If not X < Y, P(X) >= P(Y).

> Thanks,
> Mike

This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum 1994-2015. All Rights Reserved.