Abstract
We show in this note that in the forcing extension by Add(ω,iω), the following Ramsey property holds: for any r ∈ ω and any f : R → r, there exists an infinite X ⊂ R such that X + X is monochromatic under f. We also show the Ramsey statement above is true in ZFC when r = 2. This answers two questions of Komjáth et al. (2019).
| Original language | English |
|---|---|
| Pages (from-to) | 243-252 |
| Number of pages | 10 |
| Journal | Fundamenta Mathematicae |
| Volume | 250 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2020 |
Bibliographical note
Publisher Copyright:© Instytut Matematyczny PAN, 2020
Funding
The work was done when I was a graduate student at Carnegie Mellon University supported in part by the US tax payers. Part of the revision was done when I was a post doctoral fellow at Bar-Ilan University, supported by the Foreign Postdoctoral Fellowship Program of the Israel Academy of Sciences and Humanities and by the Israel Science Foundation (grant agreement 2066/18).
| Funders | Funder number |
|---|---|
| Carnegie Mellon University | |
| Israel Academy of Sciences and Humanities | |
| Israel Science Foundation | 2066/18 |
Keywords
- Additive Ramsey theory
- Forcing
- Infinite com-binatorics
- Partition relations