Baire property and axiom of choice

Haim Judah; Saharon Shelah

doi:10.1007/BF02760952

Baire property and axiom of choice

Haim Judah^*, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English
Pages (from-to)	435-450
Number of pages	16
Journal	Israel Journal of Mathematics
Volume	84
Issue number	3
DOIs	https://doi.org/10.1007/BF02760952
State	Published - Oct 1993

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author = "Haim Judah and Saharon Shelah",

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AB - 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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Baire property and axiom of choice

Abstract

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