Baire property and Axiom of Choice

Mathematics – Logic

Scientific paper

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Scientific paper

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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