Subtlety and partition relations

Toshimichi Usuba*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study the subtlety of a cardinal κ and of kΛ. We show that, under a certain large cardinal assumption, it is consistent that kΛ is subtle for some Λ > κ but κ is not subtle, and the consistency of such a situation is much stronger than the existence of a subtle cardinal. We show that the subtlety of PkΛ can be characterized by a certain partition relation on kΛ. We also study the property of faintness of κ, and the subtlety of kΛ with the strong inclusion.

Original languageEnglish
Pages (from-to)59-71
Number of pages13
JournalMathematical Logic Quarterly
Issue number1-2
Publication statusPublished - 2016 Feb 1
Externally publishedYes

ASJC Scopus subject areas

  • Logic


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