Projective measure without projective baire

David Friedman; David Schrittesser

doi:10.1090/MEMO/1298

Projective measure without projective baire

David Friedman
, David Schrittesser

School of Mathematics

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

2 Scopus citations

Abstract

We prove that it is consistent (relative to a Mahlo cardinal) that all projective sets of reals are Lebesgue measurable, but there is a Δ¹₃ set without the Baire property. The complexity of the set which provides a counterexample to the Baire property is optimal.

Original language	English
Pages (from-to)	1-62
Number of pages	62
Journal	Memoirs of the American Mathematical Society
Volume	267
Issue number	1298
DOIs	https://doi.org/10.1090/MEMO/1298
State	Published - Sep 2020

Keywords

Baire property
Forcing
Lebesgue measure
Mahlo cardinals
Projective sets

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10.1090/MEMO/1298

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title = "Projective measure without projective baire",

abstract = "We prove that it is consistent (relative to a Mahlo cardinal) that all projective sets of reals are Lebesgue measurable, but there is a Δ13 set without the Baire property. The complexity of the set which provides a counterexample to the Baire property is optimal.",

keywords = "Baire property, Forcing, Lebesgue measure, Mahlo cardinals, Projective sets",

author = "David Friedman and David Schrittesser",

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AU - Schrittesser, David

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AB - We prove that it is consistent (relative to a Mahlo cardinal) that all projective sets of reals are Lebesgue measurable, but there is a Δ13 set without the Baire property. The complexity of the set which provides a counterexample to the Baire property is optimal.

KW - Baire property

KW - Forcing

KW - Lebesgue measure

KW - Mahlo cardinals

KW - Projective sets

UR - https://www.scopus.com/pages/publications/85094072781

U2 - 10.1090/MEMO/1298

DO - 10.1090/MEMO/1298

M3 - 文章

AN - SCOPUS:85094072781

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JF - Memoirs of the American Mathematical Society

IS - 1298

ER -

Projective measure without projective baire

Abstract

Keywords

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