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Finite powers and products of Menger sets

Volume 253 / 2021

Piotr Szewczak, Boaz Tsaban, Lyubomyr Zdomskyy Fundamenta Mathematicae 253 (2021), 257-275 MSC: Primary 54D20; Secondary 03E17. DOI: 10.4064/fm896-4-2020 Published online: 25 November 2020


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.


  • Piotr SzewczakInstitute of Mathematics
    Faculty of Mathematics and Natural Sciences
    College of Sciences
    Cardinal Stefan Wyszyński University in Warsaw
    Wóycickiego 1/3
    01-938 Warszawa, Poland
    Department of Mathematics
    Bar-Ilan University
    Ramat Gan 5290002, Israel
  • Boaz TsabanDepartment of Mathematics
    Bar-Ilan University
    Ramat Gan 5290002, Israel
  • Lyubomyr ZdomskyyKurt Gödel Research Center for Mathematical Logic
    University of Vienna
    Währinger Straße 25
    A-1090 Wien, Austria

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