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On the strength of no normal precipitous filter

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Abstract

We consider a question of T. Jech and K. Prikry that asks if the existence of a precipitous filter implies the existence of a normal precipitous filter. The aim of this paper is to improve a result of Gitik (Israel J Math, 175:191–219, 2010) and to show that measurable cardinals of a higher order rather than just measurable cardinals are necessary in order to have a model with a precipitous filter but without a normal one.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

    Moti Gitik & Liad Tal

Authors
  1. Moti Gitik
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  2. Liad Tal
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Correspondence to Moti Gitik.

Additional information

Moti Gitik—partly by ISF Grant 234/08.

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Gitik, M., Tal, L. On the strength of no normal precipitous filter. Arch. Math. Logic 50, 223–243 (2011). https://doi.org/10.1007/s00153-010-0211-x

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  • DOI: https://doi.org/10.1007/s00153-010-0211-x

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Mathematics Subject Classification (2000)