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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A consistent consequence of AD
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by E. L. Bull and E. M. Kleinberg PDF
Trans. Amer. Math. Soc. 247 (1979), 211-226 Request permission

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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Additional Information
  • © Copyright 1979 American Mathematical Society
  • 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