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Baire property and axiom of choice

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This article was retracted on 27 October 2020

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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.

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Change history

  • 27 October 2020

    I hereby retract the paper [1] as the proof has an irreparable gap.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science Abraham Fraenkel Center for Mathematical Logic, Bar-Ilan University, 52900, Ramat-Gan, Israel

    Haim Judah

  2. Institute of Mathematics, The Hebrew University of Jerusalem, 91904, Jerusalem, Israel

    Saharon Shelah

Authors
  1. Haim Judah
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  2. Saharon Shelah
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Additional information

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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Judah, H., Shelah, S. Baire property and axiom of choice. Israel J. Math. 84, 435–450 (1993). https://doi.org/10.1007/BF02760952

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  • DOI: https://doi.org/10.1007/BF02760952

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