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On the non-existence of \(\kappa \)-mad families

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Abstract

Starting from a model with a Laver-indestructible supercompact cardinal \(\kappa \), we construct a model of \(ZF+DC_{\kappa }\) where there are no \(\kappa \)-mad families.

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Bahen Centre, 40 St. George St., Room 6290, Toronto, ON, M5S 2E4, Canada

    Haim Horowitz

  2. Einstein Institute of Mathematics, Edmond J. Safra Campus, The Hebrew University of Jerusalem, 91904, Givat Ram, Jerusalem, Israel

    Saharon Shelah

  3. Department of Mathematics, Hill Center - Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, NJ, 08854-8019, USA

    Saharon Shelah

Authors
  1. Haim Horowitz
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  2. Saharon Shelah
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Correspondence to Haim Horowitz.

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Publication 1168 of the second author. Date: June 12, 2019.

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Horowitz, H., Shelah, S. On the non-existence of \(\kappa \)-mad families. Arch. Math. Logic 62, 1033–1039 (2023). https://doi.org/10.1007/s00153-023-00874-6

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  • DOI: https://doi.org/10.1007/s00153-023-00874-6

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