# 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 $$NS_{\kappa ,\lambda }^{[\delta ]^{<\theta }}$$.
Document type :
Journal articles
Domain :

https://hal-normandie-univ.archives-ouvertes.fr/hal-02145582
Contributor : Pierre Matet <>
Submitted on : Monday, June 3, 2019 - 10:23:03 AM
Last modification on : Monday, April 27, 2020 - 4:14:03 PM

### Citation

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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