Finite powers and products of Menger sets

Piotr Szewczak, Boaz Tsaban, Lyubomyr Zdomskyy

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We construct, using mild combinatorial hypotheses, a real Menger set that is not Scheepers, and two real sets that are Menger in all finite powers, with a non-Menger product. By a forcing-theoretic argument, we show that the same holds in the Blass-Shelah model for arbitrary values of the ultrafilter number and the dominating number.

Original languageEnglish
Pages (from-to)257-275
Number of pages19
JournalFundamenta Mathematicae
Volume253
Issue number3
DOIs
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© 2021 Instytut Matematyczny PAN.

Keywords

  • Additivity number
  • Menger property
  • Products of concentrated sets
  • Reaping number
  • Scales
  • Scheepers property

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