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TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 249, Number 1, April 1979
ON THE EXISTENCE OF NONREGULAR ULTRAFILTERS AND THE CARDINALITYOF ULTRAPOWERS BY MENACHEM MAGIDOR Abstract. Assuming the consistency of huge cardinals, we prove that }and with truth value 1 {/(a)|a namely those sets that either them or their complement is in 'S [ b. Also every subset of i>K(/((c)) is measurable with respect to at least one of these measures. Since the cardinality of the family of these measures is at most the cardinality of {b\b G/(B)/Z)} which is/( ¿)/U. On a set in U the structures that appear in the product are countable, hence by the first part of the proof, the ultraproduct has cardinality < co3. Thus we proved that œp"ui(P) = k.
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