Stationary and closed rainbow subsets

Shimon Garti, Jing Zhang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We study the structural rainbow Ramsey theory at uncountable cardinals. Compared to the usual rainbow Ramsey theory, the variation focuses on finding a rainbow subset that not only is of a certain cardinality but also satisfies certain structural constraints, such as being stationary or closed in its supremum. In the process of dealing with cardinals greater than ω1, we uncover some connections between versions of Chang's Conjectures and instances of rainbow Ramsey partition relations, addressing a question raised in [18].

Original languageEnglish
Article number102887
JournalAnnals of Pure and Applied Logic
Volume172
Issue number2
DOIs
StatePublished - Feb 2021
Externally publishedYes

Bibliographical note

Funding Information:
Zhang is 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).

Publisher Copyright:
© 2020 Elsevier B.V.

Keywords

  • Chang's Conjecture
  • Huge cardinals
  • Martin's Maximum
  • Proper forcing axiom
  • Rainbow sets
  • Ramsey theory

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