## 抄録

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 P_{κ} λ such that NS_{κ λ} | S, the ideal generated by the non-stationary ideal NS_{κ λ} over P_{κ} λ together with P_{κ} 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 NS_{κ λ} | S (κ, λ) λ^{+}-saturated, where S (κ, λ) is the set of all x ∈ P_{κ} 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 NS_{κ λ} | S (κ, λ) is κ^{+}-saturated but GCH fails. We show that if S {set minus} S (κ, λ) is stationary in P_{κ} λ, then S can be split into λ many disjoint stationary subsets.

本文言語 | English |
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ページ（範囲） | 100-123 |

ページ数 | 24 |

ジャーナル | Annals of Pure and Applied Logic |

巻 | 149 |

号 | 1-3 |

DOI | |

出版ステータス | Published - 2007 11月 |

外部発表 | はい |

## ASJC Scopus subject areas

- 論理

## フィンガープリント

「Local saturation of the non-stationary ideal over P_{κ}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。