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On the class of measurable cardinals without the axiom of choice

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Abstract

Using techniques of Gitik in conjunction with a large cardinal hypothesis whose consistency strength is strictly in between that of a supercompact and an almost huge cardinal, we obtain the relative consistency of the theory “ZF+⇁AC w+κ>ω is measurable iffκ is the successor of a singular cardinal”.

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Authors and Affiliations

  1. Department of Mathematics, Baruch College of CUNY, 10010, New York, New York, U.S.A.

    Arthur W. Apter

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  1. Arthur W. Apter
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Apter, A.W. On the class of measurable cardinals without the axiom of choice. Israel J. Math. 79, 367–379 (1992). https://doi.org/10.1007/BF02808226

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  • DOI: https://doi.org/10.1007/BF02808226

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