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

Access to Document

10.1007/BF02760952

Cite this

@article{eee190b9e3d14c1aa49ee77307aa1d82,

title = "Baire property and axiom of choice",

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.",

author = "Haim Judah and Saharon Shelah",

year = "1993",

month = oct,

doi = "10.1007/BF02760952",

language = "אנגלית",

volume = "84",

pages = "435--450",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Baire property and axiom of choice

AU - Judah, Haim

AU - Shelah, Saharon

PY - 1993/10

Y1 - 1993/10

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=51249164143&partnerID=8YFLogxK

U2 - 10.1007/BF02760952

DO - 10.1007/BF02760952

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:51249164143

SN - 0021-2172

VL - 84

SP - 435

EP - 450

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 3

ER -

Baire property and axiom of choice

Abstract

Access to Document

Other files and links

Fingerprint

Cite this