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Intersection of ultrafilters may have measure zero

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Abstract

We show that it is consistent with ZFC that the intersection of some family of less than

ultrafilters have measure zero. This answers a question of D. Fremlin.

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References

  • [Ba] Bartoszynski, T.: On the structure of measurable filters on a countable set. Real Anal. Exch,17 (2)

  • [F] Fremlin, D.: Note of Aug. 16, 1982 (unpublished)

  • [P] Plewik, S.: Intersections and unions of ultrafilters without Baire property. Bull. Pol. Acad. Sci. Math.35, 805 (1987)

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  • [T] Talagrand, M.: Compacts de fonctions mesurables et filtres non-mesurables. Stud. Math., T.LXVII. 13–43 (1980)

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Authors and Affiliations

  1. Department of Mathematics, Boise State University, 83725, Boise, ID, USA

    Tomek Bartoszynski

  2. Department of Mathematics, The Hebrew University, Jerusalem, Israel

    Tomek Bartoszynski & Saharon Shelah

Authors
  1. Tomek Bartoszynski
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  2. Saharon Shelah
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Additional information

The author thanks the Lady Davis Fellowship Trust for full support

Partially supported by Basic Research Fund, Israel Academy of Sciences, publication 436

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Bartoszynski, T., Shelah, S. Intersection of ultrafilters may have measure zero. Arch Math Logic 31, 221–226 (1992). https://doi.org/10.1007/BF01794979

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  • DOI: https://doi.org/10.1007/BF01794979

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