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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9947-1979-0517692-2
MathSciNet review: 517692
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Abstract: We are concerned with the existence of a normal measure concentrating on the $ \omega $-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, $ {\aleph _2}$ may admit exactly two normal measures: one which contains the $ \omega $-closed unbounded sets and the other, the $ {\aleph _1}$-closed unbounded sets. This property of $ {\aleph _2}$ 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

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