New combinatorial principle on singular cardinals and normal ideals

Toshimichi Usuba*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We introduce a new combinatorial principle on singular cardinals. This principle allows us to take a kind of a diagonal intersection of more than λ many measure one sets of certain normal ideals over ℘(λ). Under the principle, we give various characterizations of the saturation property of normal ideals over ℘(λ). We also consider Chang's type transfer properties under the principle, and, when λ is Jónsson, we prove that every normal ideal over ℘(λ) with {x ⊆ λ : |x| = λ} measure one cannot have strong properties.

Original languageEnglish
Pages (from-to)395-408
Number of pages14
JournalMathematical Logic Quarterly
Issue number4-5
Publication statusPublished - 2018 Nov

ASJC Scopus subject areas

  • Logic


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