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September 2010 Extending Baire property by uncountably many sets.
Paweł Kawa, Janusz Pawlikowski
J. Symbolic Logic 75(3): 896-904 (September 2010). DOI: 10.2178/jsl/1278682206

Abstract

We show that for an uncountable κ in a suitable Cohen real model for any family { Aν} ν <kappa of sets of reals there is a σ-homomorphism h from the σ-algebra generated by Borel sets and the sets Aν into the algebra of Baire subsets of 2κ modulo meager sets such that for all Borel B,

B is meager iff h(B)=0.

The proof is uniform, works also for random reals and the Lebesgue measure, and in this way generalizes previous results of Carlson and Solovay for the Lebesgue measure and of Kamburelis and Zakrzewski for the Baire property.

Citation

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Paweł Kawa. Janusz Pawlikowski. "Extending Baire property by uncountably many sets.." J. Symbolic Logic 75 (3) 896 - 904, September 2010. https://doi.org/10.2178/jsl/1278682206

Information

Published: September 2010
First available in Project Euclid: 9 July 2010

zbMATH: 1200.03037
MathSciNet: MR2723773
Digital Object Identifier: 10.2178/jsl/1278682206

Subjects:
Primary: 03E35 , 54E52
Secondary: 28A05

Keywords: Baire property , Borel sets , meager , Measure zero , σ-algebra

Rights: Copyright © 2010 Association for Symbolic Logic

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Vol.75 • No. 3 • September 2010
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