### 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 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.

Original language | English |
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Pages (from-to) | 100-123 |

Number of pages | 24 |

Journal | Annals of Pure and Applied Logic |

Volume | 149 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 2007 Nov 1 |

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### Keywords

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

### ASJC Scopus subject areas

- Logic