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

The Hebrew University of Jerusalem, Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

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 - 1 Feb 2021

Keywords

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

All Science Journal Classification (ASJC) codes

Logic

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10.1016/j.apal.2020.102887

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AB - 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].

KW - Chang's Conjecture

KW - Huge cardinals

KW - Martin's Maximum

KW - Proper forcing axiom

KW - Rainbow sets

KW - Ramsey theory

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Stationary and closed rainbow subsets

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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