Journal of Symbolic Logic

Extending Baire property by uncountably many sets.

Paweł Kawa and Janusz Pawlikowski

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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.

Article information

Source
J. Symbolic Logic, Volume 75, Issue 3 (2010), 896-904.

Dates
First available in Project Euclid: 9 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1278682206

Digital Object Identifier
doi:10.2178/jsl/1278682206

Mathematical Reviews number (MathSciNet)
MR2723773

Zentralblatt MATH identifier
1200.03037

Subjects
Primary: 03E35: Consistency and independence results 54E52: Baire category, Baire spaces
Secondary: 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]

Keywords
Measure zero meager Borel sets Baire Property σ-algebra

Citation

Kawa, Paweł; Pawlikowski, Janusz. Extending Baire property by uncountably many sets. J. Symbolic Logic 75 (2010), no. 3, 896--904. doi:10.2178/jsl/1278682206. https://projecteuclid.org/euclid.jsl/1278682206


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