Baire property and Axiom of Choice
Haim Judah, Saharon Shelah
Abstract
We show that (1) If ZF is consistent then the following theory is consistent "ZF + DC(omega1) + 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 omega1 meager sets is meager' ".
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