IDEALS OVER UNCOUNTABLE SETS
Theorem 7.2.1. Assume that K-. carries a nonregular ultrafilter. Then
a) If N, 2 u N then 2 = 2 .
1 w1
x X
0)
b) If N is a strong limit then 2 K .
H0
Under the same assumption, Benda and Ketonen proved in [3] that 2 = H
implies 2 = tf .
Some of the results presented in this paper were announced in [8].
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