Finite powers and products of Menger sets
Volume 253 / 2021
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.