Lower bounds on coloring numbers from hardness hypotheses in PCF theory

Saharon Shelah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We prove that the statement “for every infinite cardinal κ, every graph with list-chromatic number κ has coloring number at most ℶω (κ)” proved by Kojman (2014) using the RGCH theorem implies the WRGCH theorem, which is a weaker relative of the RGCH, via a short forcing argument. Similarly, a better upper bound than ℶω (κ) in this statement implies stronger (consistent) forms of the WRGCH theorem, the consistency of whose negations is wide open. Thus, the optimality of Kojman’s upper bound is a purely cardinal arithmetic problem, and, as discussed below, is hard to decide.

Original languageEnglish
Pages (from-to)5371-5383
Number of pages13
JournalProceedings of the American Mathematical Society
Volume144
Issue number12
DOIs
StatePublished - 2016

Bibliographical note

Publisher Copyright:
© 2016 American Mathematical Society.

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