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.independent

Topic: Number of Ultrafilters
Replies: 2   Last Post: Dec 8, 2013 2:20 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
William Elliot

Posts: 1,437
Registered: 1/8/12
Number of Ultrafilters
Posted: Dec 7, 2013 2:51 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Let S be an infinite set with cardinality kappa.

If F is an ultrafilter for S, then |F| = 2^kappa.
That's proven by using the bijection f:F -> P(S)\F, A -> S\A.

If F is a filter for S, then F subset P(S) and the
collection of filters for S is a subset of P(P(S)).

How would one prove, the number of ultrafilters is exactly 2^2^kappa?





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

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.