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




Number of Ultrafilters
Posted:
Dec 7, 2013 2:51 AM


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?



