Local saturation of the non-stationary ideal over Pκ λ

Toshimichi Usuba*


研究成果: Article査読


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.

ジャーナルAnnals of Pure and Applied Logic
出版ステータスPublished - 2007 11月

ASJC Scopus subject areas

  • 論理


「Local saturation of the non-stationary ideal over Pκ λ」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。