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How many normal measures can $\aleph_{\omega + 1}$ carry?

Tom 191 / 2006

Arthur W. Apter Fundamenta Mathematicae 191 (2006), 57-66 MSC: 03E35, 03E55. DOI: 10.4064/fm191-1-4

Streszczenie

We show that assuming the consistency of a supercompact cardinal with a measurable cardinal above it, it is possible for ${\aleph_{\omega + 1}}$ to be measurable and to carry exactly $\tau$ normal measures, where $\tau \ge \aleph_{\omega + 2}$ is any regular cardinal. This contrasts with the fact that assuming AD + DC, ${\aleph_{\omega + 1}}$ is measurable and carries exactly three normal measures. Our proof uses the methods of \cite{AM}, along with a folklore technique and a new method due to James Cummings.

Autorzy

  • Arthur W. ApterDepartment of Mathematics
    Baruch College of CUNY
    New York, NY 10010, U.S.A.
    e-mail

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