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The extent of strength in the club filters

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Abstract

In this paper we consider whether the minimal normal filter onP κλ, the club filter, can have strong properties like saturation, pre-saturation, or cardinal preserving. We prove in a number of cases that the answer is no. In the case of saturation, Foreman and Magidor prove the answer is always no (except in the caseκ =λ = ℵ1—and in this case saturation is known to be consistent).

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Authors and Affiliations

  1. Department of Mathematics, University of Nevada, 89154-4020, Las Vegas, NV, USA

    Douglas R. Burke

  2. School of Informatics and Sciences, Nagoya University, 464-8601, Nagoya, Japan

    Yo Matsubara

Authors
  1. Douglas R. Burke
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  2. Yo Matsubara
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Corresponding author

Correspondence to Douglas R. Burke.

Additional information

The first author was partially supported by NSF grant DMS-9626212.

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Burke, D.R., Matsubara, Y. The extent of strength in the club filters. Isr. J. Math. 114, 253–263 (1999). https://doi.org/10.1007/BF02785581

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  • DOI: https://doi.org/10.1007/BF02785581

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