Splitting stationary sets in Pκλ for λ with small cofinality

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Abstract

For a regular uncountable cardinal κ and a cardinal λ with cf (λ) <κ <λ, we investigate the consistency strength of the existence of a stationary set in P κλ which cannot be split into λ+ many pairwise disjoint stationary subsets. To do this, we introduce a new notion for ideals, which is a variation of normality of ideals. We also prove that there is a stationary set S in Pκλ such that every stationary subset of S can be split into λ+ many pairwise disjoint stationary subsets.

Original languageEnglish
Pages (from-to)265-287
Number of pages23
JournalFundamenta Mathematicae
Volume205
Issue number3
DOIs
Publication statusPublished - 2009
Externally publishedYes

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Keywords

  • Pcf-theory
  • Stationary set

ASJC Scopus subject areas

  • Algebra and Number Theory

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