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Cofinality of normal ideals on [λ]<κ I

Abstract : An ideal J on \([\lambda ]^{<\kappa }\) is said to be \([\delta ]^{<\theta }\)-normal, where \(\delta \) is an ordinal less than or equal to \(\lambda \), and \(\theta \) a cardinal less than or equal to \(\kappa \), if given \(B_e \in J\) for \(e \in [\delta ]^{<\theta }\), the set of all \(a \in [\lambda ]^{<\kappa }\) such that \(a \in B_e\) for some \(e \in [a \cap \delta ]^{< \vert a \cap \theta \vert }\) lies in J. We give necessary and sufficient conditions for the existence of such ideals and describe the smallest one, denoted by \(NS_{\kappa ,\lambda }^{[\delta ]^{<\theta }}\). We compute the cofinality of \(NS_{\kappa ,\lambda }^{[\delta ]^{<\theta }}\).
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Submitted on : Monday, June 3, 2019 - 10:23:03 AM
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Pierre Matet, Cédric Péan, Saharon Shelah. Cofinality of normal ideals on [λ]<κ I. Archive for Mathematical Logic, Springer Verlag, 2016, 55 (5-6), pp.799-834. ⟨10.1007/s00153-016-0496-5⟩. ⟨hal-02145582⟩



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