Stationary and closed rainbow subsets

Shimon Garti; Jing Zhang

doi:10.1016/j.apal.2020.102887

Stationary and closed rainbow subsets

Shimon Garti, Jing Zhang^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Article number	102887
Pages (from-to)	1-16
Number of pages	16
Journal	Annals of Pure and Applied Logic
Volume	172
Issue number	2
DOIs	https://doi.org/10.1016/j.apal.2020.102887
State	Published - Feb 2021

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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10.1016/j.apal.2020.102887

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Stationary and closed rainbow subsets

Abstract

Bibliographical note

Keywords

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