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