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Baire property and Axiom of Choice

Haim Judah·Saharon Shelah
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Abstract

We show that (1) If ZF is consistent then the following theory is consistent "ZF + DC(omega_{1}) + Every set of reals has Baire property" and (2) If ZF is consistent then the following theory is consistent "ZFC + `every projective set of reals has Baire property' + `any union of omega_{1} meager sets is meager' ".

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Haim Judah, Saharon Shelah. 1992-11-15. Baire property and Axiom of Choice. https://arxiv.org/abs/math/9211213

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