Abstract
We address the question of whether a reflecting stationary set may be partitioned into two or more reflecting stationary subsets, providing various affirmative answers in ZFC. As an application to singular cardinal combinatorics, we infer that it is never the case that there exists a singular cardinal all of whose scales are very good.
| Original language | English |
|---|---|
| Pages (from-to) | 3551-3565 |
| Number of pages | 15 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 148 |
| Issue number | 8 |
| DOIs | |
| State | Published - Aug 2020 |
Bibliographical note
Publisher Copyright:© 2020 American Mathematical Society
Funding
Received by the editors February 15, 2019, and, in revised form, July 19, 2019. 2010 Mathematics Subject Classification. Primary 03E05; Secondary 03E04. Key words and phrases. Reflecting stationary set, very good scale, Ulam matrix, club guessing. The second author was partially supported by the European Research Council (grant agreement ERC-2018-StG 802756) and by the Israel Science Foundation (grant agreement 2066/18).
| Funders | Funder number |
|---|---|
| Horizon 2020 Framework Programme | 802756 |
| European Commission | |
| Israel Science Foundation | 2066/18 |
Keywords
- Club guessing
- Reflecting stationary set
- Ulam matrix
- Very good scale