Geodesic
How many normal measures can $\aleph_{\omega + 1}$ carry?
Arthur W. Apter1
1 Department of Mathematics Baruch College of CUNY New York, NY 10010, U.S.A.
Fundamenta Mathematicae, Tome 191 (2006) no. 1, pp. 57-66

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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.
DOI : 10.4064/fm191-1-4
Keywords: assuming consistency supercompact cardinal measurable cardinal above possible aleph omega measurable carry exactly tau normal measures where tau aleph omega regular cardinal contrasts assuming aleph omega measurable carries exactly three normal measures proof uses methods cite along folklore technique method due james cummings

Arthur W. Apter 1

1 Department of Mathematics Baruch College of CUNY New York, NY 10010, U.S.A. 
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Arthur W. Apter. How many normal measures can $\aleph_{\omega + 1}$ carry?. Fundamenta Mathematicae, Tome 191 (2006) no. 1, pp. 57-66. doi: 10.4064/fm191-1-4

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