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Archive for Mathematical Logic

, Volume 55, Issue 5–6, pp 799–834 | Cite as

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

  • Pierre MatetEmail author
  • Cédric Péan
  • Saharon Shelah
Article
  • 42 Downloads

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 \(NS_{\kappa ,\lambda }^{[\delta ]^{<\theta }}\).

Keywords

\([\lambda ]^{<\kappa }\) Normal ideal 

Mathematics Subject Classification

03E05 03E55 03E35 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques, CNRSUniversité de CaenCaen CedexFrance
  2. 2.NexwaysParisFrance
  3. 3.Einstein Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael
  4. 4.Department of Mathematics, Hill Center for the Mathematical SciencesRutgers UniversityPiscatawayUSA

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