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arXiv · 1903.03170

Finite powers and products of Menger sets

Piotr Szewczak·Boaz Tsaban·Lyubomyr Zdomskyy
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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 and dominating number.

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Piotr Szewczak, Boaz Tsaban, Lyubomyr Zdomskyy. 2019-03-07. Finite powers and products of Menger sets. https://arxiv.org/abs/1903.03170

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