Real Analysis Exchange

On Borel Hull Operations

Tomasz Filipczak, Andrzej Rosłanowski, and Saharon Shelah

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Abstract

We show that some set-theoretic assumptions (for example Martin’s Axiom) imply that there is no translation invariant Borel hull operation on the family of Lebesgue null sets and on the family of meager sets (in \(\mathbb{R}^{n}\)). We also prove that if the meager ideal admits a monotone Borel hull operation, then there is also a monotone Borel hull operation on the \(\sigma\)-algebra of sets with the property of Baire.

Article information

Source
Real Anal. Exchange, Volume 40, Number 1 (2015), 129-140.

Dates
First available in Project Euclid: 1 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.rae/1435759199

Mathematical Reviews number (MathSciNet)
MR3365394

Zentralblatt MATH identifier
06848827

Subjects
Primary: 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05] 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]
Secondary: 03E15: Descriptive set theory [See also 28A05, 54H05] 03E17: Cardinal characteristics of the continuum

Keywords
meager ideal null ideal Borel hull

Citation

Filipczak, Tomasz; Rosłanowski, Andrzej; Shelah, Saharon. On Borel Hull Operations. Real Anal. Exchange 40 (2015), no. 1, 129--140. https://projecteuclid.org/euclid.rae/1435759199


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