Journal of Symbolic Logic

Extending Baire property by uncountably many sets.

Paweł Kawa and Janusz Pawlikowski

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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

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

First available in Project Euclid: 9 July 2010

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

Measure zero meager Borel sets Baire Property σ-algebra


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.

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