Splitting stationary sets in p(λ)

Toshimichi Usuba*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Let A be a non-empty set. A set S ⊆ P (A) is said to be stationary in P(A) if for every f: [A]<ω → A there exists x ∈ S such that x ≠ A and f"[x]<ω ⊆ x. In this paper we prove the following: For an uncountable cardinal λ and a stationary set S in P(λ), if there is a regular uncountable cardinal k ≤ λ such that {x ∈ S : x ∩ k ∈ k} is stationary, then S can be split into k disjoint stationary subsets.

Original languageEnglish
Pages (from-to)49-62
Number of pages14
JournalJournal of Symbolic Logic
Issue number1
Publication statusPublished - 2012 Mar
Externally publishedYes


  • Pcf-theory
  • Saturated ideal
  • Stationary set

ASJC Scopus subject areas

  • Philosophy
  • Logic


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