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Cofinality of normal ideals on \([\lambda ]^{<\kappa }\) I

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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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Correspondence to Pierre Matet.

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Cédric Péan: Some of the material in this paper originally appeared as part of the author’s doctoral dissertation completed at the Université de Caen, 1998.

Saharon Shelah: Partially supported by the Israel Science Foundation. Publication 713.

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Matet, P., Péan, C. & Shelah, S. Cofinality of normal ideals on \([\lambda ]^{<\kappa }\) I. Arch. Math. Logic 55, 799–834 (2016). https://doi.org/10.1007/s00153-016-0496-5

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  • DOI: https://doi.org/10.1007/s00153-016-0496-5

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