Menas’ Result is Best Possible

Apter, Arthur; Shelah, Saharon

doi:10.1090/S0002-9947-97-01691-7

Menas' Result is Best Possible

Authors: Arthur W. Apter and Saharon Shelah
Journal: Trans. Amer. Math. Soc. 349 (1997), 2007-2034
MSC (1991): Primary 03E55; Secondary 03E35
DOI: https://doi.org/10.1090/S0002-9947-97-01691-7
MathSciNet review: 1370634
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Abstract: Generalizing some earlier techniques due to the second author, we show that Menas' theorem which states that the least cardinal $\kappa$ which is a measurable limit of supercompact or strongly compact cardinals is strongly compact but not $2^{\kappa }$ supercompact is best possible. Using these same techniques, we also extend and give a new proof of a theorem of Woodin and extend and give a new proof of an unpublished theorem due to the first author.

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Additional Information

Arthur W. Apter
Affiliation: Department of Mathematics, Baruch College of CUNY, New York, New York 10010
Email: awabb@cunyvm.cuny.edu

Saharon Shelah
Affiliation: Department of Mathematics, The Hebrew University, Jerusalem, Israel; Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08904
Email: shelah@math.huji.ac.il, shelah@math.rutgers.edu

DOI: https://doi.org/10.1090/S0002-9947-97-01691-7
Received by editor(s): March 3, 1995
Received by editor(s) in revised form: December 13, 1995
Additional Notes: The research of the first author was partially supported by PSC-CUNY Grant 662341 and a salary grant from Tel Aviv University. In addition, the first author wishes to thank the Mathematics Departments of Hebrew University and Tel Aviv University for the hospitality shown him during his sabbatical in Israel.
Publication 496. The second author wishes to thank the Basic Research Fund of the Israeli Academy of Sciences for partially supporting this research.
Article copyright: © Copyright 1997 American Mathematical Society