## Menas’ Result is Best Possible

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- by Arthur W. Apter and Saharon Shelah PDF
- Trans. Amer. Math. Soc.
**349**(1997), 2007-2034 Request permission

## 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these same techniques, we also extend and give a new proof of a theorem of Woodin and extend and give a new proof of an unpublished theorem due to the first author.## References

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## Additional Information

**Arthur W. Apter**- Affiliation: Department of Mathematics, Baruch College of CUNY, New York, New York 10010
- MR Author ID: 26680
- 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
- MR Author ID: 160185
- ORCID: 0000-0003-0462-3152
- Email: shelah@math.huji.ac.il, shelah@math.rutgers.edu
- 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. - © Copyright 1997 American Mathematical Society
- 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