Abstract
It is proved that a strong instance of the guessing principle ♣AD on the first uncountable cardinal follows from either the principle, or the principle ♢(b), or the existence of a Luzin set. In particular, any of the above hypotheses entails the existence of a Dowker space of size ℵ1.
| Original language | English |
|---|---|
| Pages (from-to) | 102-117 |
| Number of pages | 16 |
| Journal | Periodica Mathematica Hungarica |
| Volume | 88 |
| Issue number | 1 |
| DOIs | |
| State | Published - Mar 2024 |
Bibliographical note
Publisher Copyright:© Akadémiai Kiadó, Budapest, Hungary 2023.
Funding
The first author is partially supported by the European Research Council (grant agreement ERC-2018-StG 802756) and by the Israel Science Foundation (grant agreement 203/22). The second author is supported by the European Research Council (grant agreement ERC-2018-StG 802756). The third author is partially supported by grants from NSERC (455916), CNRS (IMJ-PRG UMR7586) and SFRS (7750027-SMART).
| Funders | Funder number |
|---|---|
| Natural Sciences and Engineering Research Council of Canada | |
| European Commission | ERC-2018-StG 802756 |
| Israel Science Foundation | 203/22 |
| Centre National de la Recherche Scientifique | 7750027-SMART, IMJ-PRG UMR7586 |
Keywords
- 54G20
- Club AD
- Dowker space
- Luzin set
- Primary 03E05
- Secondary 03E65
- Stick
- Strongly unbounded coloring