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Set theory without choice: not everything on cofinality is possible

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Abstract.

We prove in ZF+DC, e.g. that: if \(\mu=|{\cal H}(\mu)|\) and \(\mu>\cf(\mu)>\aleph_0\) then \(\mu ^+\) is regular but non measurable. This is in contrast with the results on measurability for \(\mu=\aleph_\omega\) due to Apter and Magidor [ApMg].

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel, , , , , , IL

    Saharon Shelah

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  1. Saharon Shelah
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Received May 6, 1993 / Revised December 11, 1995

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Shelah, S. Set theory without choice: not everything on cofinality is possible . Arch Math Logic 36, 81–125 (1997). https://doi.org/10.1007/s001530050057

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  • DOI: https://doi.org/10.1007/s001530050057