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.
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© 2021 Instytut Matematyczny PAN.
- Additivity number
- Menger property
- Products of concentrated sets
- Reaping number
- Scheepers property