Borel extensions of Baire measures in ZF

Menachem Kojman, Henryk Michalewski

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)197-223
Number of pages27
JournalFundamenta Mathematicae
Volume211
Issue number3
DOIs
StatePublished - 13 Jul 2011

Keywords

  • Baire measure
  • Dowker space
  • Measure extension problem
  • PCF theory

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