Non‐saturation of the non‐stationary ideal on Pκ (λ) with λ of countable cofinality

Mathematical Logic Quarterly 58 (1-2):38-45 (2012)

Given a regular uncountable cardinal κ and a cardinal λ > κ of cofinality ω, we show that the restriction of the non-stationary ideal on Pκ to the set of all a with equation image is not λ++-saturated . We actually prove the stronger result that there is equation image with |Q| = λ++ such that A∩B is a non-cofinal subset of Pκ for any two distinct members A, B of Q, where NGκ, λ denotes the game ideal on Pκ. We also remark that for κ > ω1, adding λ+3 Cohen subsets of ω1 to equation image makes NGκ, λ λ+3-saturated
Keywords saturation  MSC (2010) 03E05  Pκ(λ)
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DOI 10.1002/malq.201020055
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References found in this work BETA

Weak Saturation of Ideals on Pκ(Λ).Pierre Matet - 2011 - Mathematical Logic Quarterly 57 (2):149-165.
Game Ideals.Pierre Matet - 2009 - Annals of Pure and Applied Logic 158 (1-2):23-39.

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Guessing More Sets.Pierre Matet - 2015 - Annals of Pure and Applied Logic 166 (10):953-990.

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