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.
| Original language | English |
|---|---|
| Pages (from-to) | 257-275 |
| Number of pages | 19 |
| Journal | Fundamenta Mathematicae |
| Volume | 253 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2021 |
Bibliographical note
Publisher Copyright:© 2021 Instytut Matematyczny PAN.
Funding
third named author for his kind hospitality at the Kurt Gödel Research Center in fall 2016. We also thank the Center’s Director, researchers and staff for the excellent academic and friendly atmosphere. The third named author would like to thank the Austrian Science Fund FWF (Grants I 2374-N35 and I 3709-N35) for generous support for this research. We are also grateful to the anonymous referee for careful reading of the manuscript.
| Funders | Funder number |
|---|---|
| Austrian Science Fund | I 3709-N35, I 2374-N35 |
Keywords
- Additivity number
- Menger property
- Products of concentrated sets
- Reaping number
- Scales
- Scheepers property