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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1111433-9
PII: S 0002-9939(1993)1111433-9
Article copyright: © Copyright 1993 American Mathematical Society