PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

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

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.

Authors

  • 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
    and
    Department of Mathematics
    Bar-Ilan University
    Ramat Gan 5290002, Israel
    e-mail
  • Boaz TsabanDepartment of Mathematics
    Bar-Ilan University
    Ramat Gan 5290002, Israel
    e-mail
  • Lyubomyr ZdomskyyKurt Gödel Research Center for Mathematical Logic
    University of Vienna
    Währinger Straße 25
    A-1090 Wien, Austria
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image