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

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William Elliot

Posts: 2,637
Registered: 1/8/12
Number of Ultrafilters
Posted: Dec 7, 2013 2:51 AM
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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?

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