Non-saturation of the nonstationary ideal on P κ (λ) in case κ≤ cf (λ)< λ

Archive for Mathematical Logic 51 (3-4):425-432 (2012)

Abstract

Given a regular cardinal κ > ω 1 and a cardinal λ with κ ≤ cf (λ) < λ, we show that NS κ,λ | T is not λ+-saturated, where T is the set of all ${a\in P_\kappa (\lambda)}$ such that ${| a | = | a \cap \kappa|}$ and ${{\rm cf} \big( {\rm sup} (a\cap\kappa)\big) = {\rm cf} \big({\rm sup} (a)\big) = \omega}$

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References found in this work

Game Ideals.Pierre Matet - 2009 - Annals of Pure and Applied Logic 158 (1-2):23-39.
The Magidor Function and Diamond.Pierre Matet - 2011 - Journal of Symbolic Logic 76 (2):405 - 417.
Introduction to Cardinal Arithmetic.Maxim Burke - 2002 - Bulletin of Symbolic Logic 8 (4):524-526.

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