Non-saturation of the nonstationary ideal on Pκ(λ) in case κ ≤ cf (λ) < λ

Archive for Mathematical Logic 51 (3-4):425-432 (2012)
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Abstract

Given a regular cardinal κ > ω1 and a cardinal λ with κ ≤ cf (λ) < λ, we show that NSκ,λ | T is not λ+-saturated, where T is the set of all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${a\in P_\kappa (\lambda)}$$\end{document} such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${| a | = | a \cap \kappa|}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm cf} \big( {\rm sup} (a\cap\kappa)\big) = {\rm cf} \big({\rm sup} (a)\big) = \omega}$$\end{document}.

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The Magidor function and diamond.Pierre Matet - 2011 - Journal of Symbolic Logic 76 (2):405 - 417.
Introduction to Cardinal Arithmetic.Maxim Burke - 2002 - Bulletin of Symbolic Logic 8 (4):524-526.

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