Local saturation of the non-stationary ideal over Pκ λ

Research output: Contribution to journalArticle

Abstract

Starting with a λ-supercompact cardinal κ, where λ is a regular cardinal greater than or equal to κ, we produce a model with a stationary subset S of Pκ λ such that NSκ λ | S, the ideal generated by the non-stationary ideal NSκ λ over Pκ λ together with Pκ λ {set minus} S, is λ+-saturated. Using this model we prove the consistency of the existence of such a stationary set together with the Generalized Continuum Hypothesis (GCH). We also show that in our model we can make NSκ λ | S (κ, λ) λ+-saturated, where S (κ, λ) is the set of all x ∈ Pκ λ such that ot (x), the order type of x, is a regular cardinal and x is stationary in sup (x). Furthermore we construct a model where NSκ λ | S (κ, λ) is κ+-saturated but GCH fails. We show that if S {set minus} S (κ, λ) is stationary in Pκ λ, then S can be split into λ many disjoint stationary subsets.

Original languageEnglish
Pages (from-to)100-123
Number of pages24
JournalAnnals of Pure and Applied Logic
Volume149
Issue number1-3
DOIs
Publication statusPublished - 2007 Nov 1
Externally publishedYes

Keywords

  • Club-shooting
  • GCH
  • Non-stationary ideal
  • P λ
  • Saturated ideal

ASJC Scopus subject areas

  • Logic

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