Borel extensions of Baire measures in ZF

Menachem Kojman; Henryk Michalewski

doi:10.4064/fm211-3-1

Borel extensions of Baire measures in ZF

Menachem Kojman, Henryk Michalewski

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove: (1) Every Baire measure on the Kojman-Shelah Dowker space admits a Borel exten- sion. (2) If the continuum is not real-valued-measurable then every Baire measure on M. E. Rudin's Dowker space admits a Borel extension. Consequently, Balogh's space remains the only candidate to be a ZFC counterexample to the measure extension problem of the three presently known ZFC Dowker spaces.

Original language	English
Pages (from-to)	197-223
Number of pages	27
Journal	Fundamenta Mathematicae
Volume	211
Issue number	3
DOIs	https://doi.org/10.4064/fm211-3-1
State	Published - 13 Jul 2011

Keywords

Baire measure
Dowker space
Measure extension problem
PCF theory

ASJC Scopus subject areas

Algebra and Number Theory

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10.4064/fm211-3-1

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KW - PCF theory

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Borel extensions of Baire measures in ZF

Abstract

Keywords

ASJC Scopus subject areas

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