Two-cardinal versions of weak compactness: Partitions of triples

Pierre Matet*, Toshimichi Usuba

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Let k be a regular uncountable cardinal, and λ be a cardinal greater than k. Our main result asserts that if (λ<k)<(λ<k) = λ<k, then (pk,λ(NInk,λ<k))+ → + (NS[λ]<k k;λ )+; NSk;λs+)3 and (pk,λ(NAInk;λ<k))+ → (NSk;λs+)3, where NSk;λs (respectively, NS[λ]<k k;λ) denotes the smallest seminormal (respectively, strongly normal) ideal on Pk(λ), NInk,λ<k (respectively, NAInk;λ<k) denotes the ideal of non-ineffable (respectively, non-almost ineffable) subsets of Pk(λ<k), and pk,λ : Pk(λ<k) → Pk(λ) is defined by pk,λ(x) = x ∩ λ.

Original languageEnglish
Pages (from-to)207-230
Number of pages24
JournalJournal of the Mathematical Society of Japan
Issue number1
Publication statusPublished - 2015
Externally publishedYes


  • Partition relation
  • Pk(λ)
  • Weakly compact cardinal

ASJC Scopus subject areas

  • Mathematics(all)


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