Monochromatic sumset without large cardinals

Jing Zhang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 languageEnglish
Pages (from-to)243-252
Number of pages10
JournalFundamenta Mathematicae
Volume250
Issue number3
DOIs
StatePublished - 2020
Externally publishedYes

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).

FundersFunder number
Carnegie Mellon University
Israel Academy of Sciences and Humanities
Israel Science Foundation2066/18

    Keywords

    • Additive Ramsey theory
    • Forcing
    • Infinite com-binatorics
    • Partition relations

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