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All meager filters may be null


Authors: Tomek Bartoszyński, Martin Goldstern, Haim Judah and Saharon Shelah
Journal: Proc. Amer. Math. Soc. 117 (1993), 515-521
MSC: Primary 03E35; Secondary 28A05, 28E15, 54A25
DOI: https://doi.org/10.1090/S0002-9939-1993-1111433-9
MathSciNet review: 1111433
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Abstract: We show that in the Cohen model the sum of two nonmeasurable sets is always nonmeager. As a consequence we show that it is consistent with ZFC that all filters which have the Baire property are Lebesgue measurable. We also show that the existence of a Sierpinski set implies that there exists a nonmeasurable filter which has the Baire property.


References [Enhancements On Off] (What's this?)

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  • [BS] A. Blass and S. Shelah, There may be simple $ {P_{{\aleph _1}}}$- and $ {P_{{\aleph _2}}}$-points and the Rudin-Keisler ordering may be downward directed, Ann. Pure Appl. Logic 33 (1987). MR 879489 (88e:03073)
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  • [T] M. Talagrand, Compacts de fonctions mesurables et filtres nonmesurables, Studia Math. 67 (1980). MR 579439 (82e:28009)

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DOI: https://doi.org/10.1090/S0002-9939-1993-1111433-9
Article copyright: © Copyright 1993 American Mathematical Society

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