All meager filters may be null

Tomek Bartoszynski; Martin Goldstern; Haim Judah; Saharon Shelah

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

All meager filters may be null

Tomek Bartoszynski
, Martin Goldstern
, Haim Judah
, Saharon Shelah

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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.

Original language	English
Pages (from-to)	515-521
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	117
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1993-1111433-9
State	Published - Feb 1993

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title = "All meager filters may be null",

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.",

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AB - 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.

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All meager filters may be null

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