Ramsey theory over partitions II: Negative Ramsey relations and pump-up theorems

Menachem Kojman, Assaf Rinot, Juris Steprāns

Research output: Contribution to journalArticlepeer-review

Abstract

In this series of papers we advance Ramsey theory over partitions. In this part, we concentrate on anti-Ramsey relations, or, as they are better known, strong colorings, and in particular solve two problems from [CKS21]. It is shown that for every infinite cardinal λ, a strong coloring on λ+ by λ colors over a partition can be stretched to one with λ+ colors over the same partition. Also, a sufficient condition is given for when a strong coloring witnessing Pr1(…) over a partition may be improved to witness Pr0(…). Since the classical theory corresponds to the special case of a partition with just one cell, the two results generalize pump-up theorems due to Eisworth and Shelah, respectively.

Original languageEnglish
JournalIsrael Journal of Mathematics
DOIs
StateAccepted/In press - 1 Jan 2023

ASJC Scopus subject areas

  • General Mathematics

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