Menas’ Result is Best Possible

Apter, Arthur; Shelah, Saharon

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

Menas’ Result is Best Possible
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by Arthur W. Apter and Saharon Shelah

Trans. Amer. Math. Soc. 349 (1997), 2007-2034

DOI: https://doi.org/10.1090/S0002-9947-97-01691-7

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same techniques, we also extend and give a new proof of a theorem of Woodin and extend and give a new proof of an unpublished theorem due to the first author.

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