Baire property and axiom of choice |
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| Authors: | Haim Judah Saharon Shelah |
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| Institution: | (1) Department of Mathematics and Computer Science Abraham Fraenkel Center for Mathematical Logic, Bar-Ilan University, 52900 Ramat-Gan, Israel;(2) Institute of Mathematics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel |
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| Abstract: | We show that without using inaccessible cardinals it is possible to get models of “ZF+all sets of reals have the Baire property
+DC(ω1)” and “ZFC+all projective sets have the Baire property+the union of less than ω2 many meager sets is meager”, answering two well-known open questions of Woodin and Judah, respectively.
The authors would like to thank the Israel Academy of Sciences BSF for partial support.
The second author would like to thank the Landau Center for Mathematical Analysis, supported by the Minerva Foundation (Germany). |
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