All meager filters may be null

Bartoszyński, Tomek; Goldstern, Martin; Judah, Haim; Shelah, Saharon

doi:10.1090/S0002-9939-1993-1111433-9

All meager filters may be null
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by Tomek Bartoszyński, Martin Goldstern, Haim Judah and Saharon Shelah

Proc. Amer. Math. Soc. 117 (1993), 515-521

DOI: https://doi.org/10.1090/S0002-9939-1993-1111433-9

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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.

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