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  1. Guessing more sets.Pierre Matet - 2015 - Annals of Pure and Applied Logic 166 (10):953-990.
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  • Two-cardinal diamond and games of uncountable length.Pierre Matet - 2015 - Archive for Mathematical Logic 54 (3-4):395-412.
    Let μ,κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu, \kappa}$$\end{document} and λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\lambda}$$\end{document} be three uncountable cardinals such that μ=cf<κ=cf<λ.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu = {\rm cf} < \kappa = {\rm cf} < \lambda.}$$\end{document} The game ideal NGκ,λμ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${NG_{\kappa,\lambda}^\mu}$$\end{document} is a normal ideal on Pκ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${P_\kappa }$$\end{document} defined using games (...)
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  • When P(λ) (vaguely) resembles κ.Pierre Matet - 2021 - Annals of Pure and Applied Logic 172 (2):102874.
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  • The secret life of μ-clubs.Pierre Matet - 2022 - Annals of Pure and Applied Logic 173 (9):103162.
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  • Towers and clubs.Pierre Matet - 2021 - Archive for Mathematical Logic 60 (6):683-719.
    We revisit several results concerning club principles and nonsaturation of the nonstationary ideal, attempting to improve them in various ways. So we typically deal with a ideal J extending the nonstationary ideal on a regular uncountable cardinal \, our goal being to witness the nonsaturation of J by the existence of towers ).
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  • Meeting numbers and pseudopowers.Pierre Matet - 2021 - Mathematical Logic Quarterly 67 (1):59-76.
    We study the role of meeting numbers in pcf theory. In particular, Shelah's Strong Hypothesis is shown to be equivalent to the assertion that for any singular cardinal σ of cofinality ω, there is a size collection Q of countable subsets of σ with the property that for any infinite subset a of σ, there is a member of Q meeting a in an infinite set.
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  • Applications of Pcf Theory to the Study of Ideals On.Pierre Matet - 2022 - Journal of Symbolic Logic 87 (3):967-994.
    Let$\kappa $be a regular uncountable cardinal, anda cardinal greater than or equal to$\kappa $. Revisiting a celebrated result of Shelah, we show that ifis close to$\kappa $and(= the least size of a cofinal subset of) is greater than, thencan be represented (in the sense of pcf theory) as a pseudopower. This can be used to obtain optimal results concerning the splitting problem. For example we show that ifand, then no$\kappa $-complete ideal onis weakly-saturated.
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