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Extending Baire property by uncountably many sets

Published online by Cambridge University Press:  12 March 2014

Paweł Kawa  and
Janusz Pawlikowski
Paweł Kawa
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Ul. Śniadeckich 8, 00-956 Warszawa, Poland. E-mail: kawa@impan.gov.pl
Janusz Pawlikowski
Affiliation:
Institute of Mathematics, University of Wroclaw, Pl. Grunwaldzki 2/4 50-384 Wroclaw., Poland. E-mail: pawlikow@math.uni.wroc.pl
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Abstract

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

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.

Keywords

Measure zeromeagerBorel setsBaire Propertyσ-algebra
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 3 , September 2010 , pp. 896 - 904
Copyright
Copyright © Association for Symbolic Logic 2010

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References

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