A consistent consequence of AD

Authors:
E. L. Bull and E. M. Kleinberg

Journal:
Trans. Amer. Math. Soc. **247** (1979), 211-226

MSC:
Primary 03E35; Secondary 03E60

MathSciNet review:
517692

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Abstract: We are concerned with the existence of a normal measure concentrating on the -closed unbounded sets. We strengthen the known result that the axiom of choice implies no such measure exists. It is shown that the existence of these measures is consistent (relative to a large cardinal). In particular, may admit exactly two normal measures: one which contains the -closed unbounded sets and the other, the -closed unbounded sets. This property of is a well-known consequence of AD.

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DOI:
https://doi.org/10.1090/S0002-9947-1979-0517692-2

Article copyright:
© Copyright 1979
American Mathematical Society