31 found
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  1.  58
    Weak Saturation of Ideals on Pκ(Λ).Pierre Matet - 2011 - Mathematical Logic Quarterly 57 (2):149-165.
    We show that if κ is an infinite successor cardinal, and λ > κ a cardinal of cofinality less than κ satisfying certain conditions, then no ideal on Pκ is weakly λ+-saturated. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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  2.  6
    When P(Λ) (Vaguely) Resembles Κ.Pierre Matet - 2021 - Annals of Pure and Applied Logic 172 (2):102874.
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  3.  7
    Game Ideals.Pierre Matet - 2009 - Annals of Pure and Applied Logic 158 (1-2):23-39.
    We study a normal ideal on Pκ that is defined in terms of games.
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  4.  22
    Ideals on $${P_{\Kappa}}$$ P Κ Associated with Games of Uncountable Length.Pierre Matet - 2015 - Archive for Mathematical Logic 54 (3-4):291-328.
    We study normal ideals 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} that are defined in terms of games of uncountable length.
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  5.  20
    The Magidor Function and Diamond.Pierre Matet - 2011 - Journal of Symbolic Logic 76 (2):405 - 417.
    Let κ be a regular uncountable cardinal and λ be a cardinal greater than κ. We show that if 2 <κ ≤ M(κ, λ), then ◇ κ,λ holds, where M(κ, λ) equals $\lambda ^{\aleph }0$ if cf(λ) ≥ κ, and $(\lambda ^{+})^{\aleph _{0}}$ otherwise.
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  6. Q-Pointness, P-Pointness and Feebleness of Ideals.Pierre Matet & Janusz Pawlikowski - 2003 - Journal of Symbolic Logic 68 (1):235-261.
    We study the degree of (weak) Q-pointness, and that of (weak) P-pointness, of ideals on a regular infinite cardinal.
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  7.  48
    Non‐Saturation of the Non‐Stationary Ideal on Pκ (Λ) with Λ of Countable Cofinality.Pierre Matet - 2012 - Mathematical Logic Quarterly 58 (1-2):38-45.
    Given a regular uncountable cardinal κ and a cardinal λ > κ of cofinality ω, we show that the restriction of the non-stationary ideal on Pκ to the set of all a with equation image is not λ++-saturated . We actually prove the stronger result that there is equation image with |Q| = λ++ such that A∩B is a non-cofinal subset of Pκ for any two distinct members A, B of Q, where NGκ, λ denotes the game ideal on Pκ. (...)
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  8.  4
    Two-Cardinal Diamond Star.Pierre Matet - 2014 - Mathematical Logic Quarterly 60 (4-5):246-265.
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  9.  12
    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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  10.  47
    Non-Saturation of the Nonstationary Ideal on P Κ (Λ) in Case Κ≤ Cf (Λ)< Λ.Pierre Matet - 2012 - Archive for Mathematical Logic 51 (3-4):425-432.
    Given a regular cardinal κ > ω 1 and a cardinal λ with κ ≤ cf (λ) < λ, we show that NS κ,λ | T is not λ+-saturated, where T is the set of all ${a\in P_\kappa (\lambda)}$ such that ${| a | = | a \cap \kappa|}$ and ${{\rm cf} \big( {\rm sup} (a\cap\kappa)\big) = {\rm cf} \big({\rm sup} (a)\big) = \omega}$.
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  11.  20
    Yoshihiro Abe. Weakly Normal Filters and the Closed Unbounded Filter on Pkλ. Proceedings of the American Mathematical Society, Vol. 104 , Pp. 1226–1234. - Yoshihiro Abe. Weakly Normal Filters and Large Cardinals. Tsukuba Journal of Mathematics, Vol. 16 , Pp. 487–494. - Yoshihiro Abe. Weakly Normal Ideals on Pkλ and the Singular Cardinal Hypothesis. Fundamenta Mathematicae, Vol. 143 , Pp. 97–106. - Yoshihiro Abe. Saturation of Fundamental Ideals on Pkλ. Journal of the Mathematical Society of Japan, Vol. 48 , Pp. 511–524. - Yoshihiro Abe. Strongly Normal Ideals on Pkλ and the Sup-Function. Opology and its Applications, Vol. 74 , Pp. 97–107. - Yoshihiro Abe. Combinatorics for Small Ideals on Pkλ. Mathematical Logic Quarterly, Vol. 43 , Pp. 541–549. - Yoshihiro Abe and Masahiro Shioya. Regularity of Ultrafilters and Fixed Points of Elementary Embeddings. Tsukuba Journal of Mathematics, Vol. 22 , Pp. 31–37. [REVIEW]Pierre Matet - 2002 - Bulletin of Symbolic Logic 8 (2):309-311.
  12.  26
    Partition Relations for Strongly Normal Ideals on Pκ(Λ).Pierre Matet - 2000 - Mathematical Logic Quarterly 46 (1):87-103.
    Building upon earlier work of Donna Carr, Don Pelletier, Chris Johnson, Shu-Guo Zhang and others, we show that a normal ideal J on Pκ is strongly normal if and only if J+→< 2 for every μ < κ, and we describe the least normal ideal J on Pκ such that J+ →< 2.
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  13.  23
    Some Aspects Ofn-Subtlety.Pierre Matet - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (2):189-192.
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  14.  16
    Prime Ideals on P Ω (Λ) with the Partition Property.Pierre Matet, Cédric Péan & Stevo Todorcevic - 2002 - Archive for Mathematical Logic 41 (8):743-764.
    . We use ideas of Fred Galvin to show that under Martin's axiom, there is a prime ideal on Pω with the partition property for every \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}.
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  15.  7
    Two-Cardinal Versions of Weak Compactness: Partitions of Pairs.Pierre Matet & Toshimichi Usuba - 2012 - Annals of Pure and Applied Logic 163 (1):1-22.
  16.  56
    A Partition Property of a Mixed Type for P~K(Lambda).Pierre Matet - 2003 - Mathematical Logic Quarterly 49 (6):615.
    Given a regular infinite cardinal κ and a cardinal λ > κ, we study fine ideals H on Pκ that satisfy the square brackets partition relation equation image, where μ is a cardinal ≥2.
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  17.  3
    Some Aspects of N‐Subtlety.Pierre Matet - 1988 - Mathematical Logic Quarterly 34 (2):189-192.
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  18.  14
    Some Filters of Partitions.Pierre Matet - 1988 - Journal of Symbolic Logic 53 (2):540-553.
  19.  17
    Combinatorics and Forcing with Distributive Ideals.Pierre Matet - 1997 - Annals of Pure and Applied Logic 86 (2):137-201.
    We present a version for κ-distributive ideals over a regular infinite cardinal κ of some of the combinatorial results of Mathias on happy families. We also study an associated notion of forcing, which is a generalization of Mathias forcing and of Prikry forcing.
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  20.  15
    Happy Families and Completely Ramsey Sets.Pierre Matet - 1993 - Archive for Mathematical Logic 32 (3):151-171.
    We use games of Kastanas to obtain a new characterization of the classC ℱ of all sets that are completely Ramsey with respect to a given happy family ℱ. We then combine this with ideas of Plewik to give a uniform proof of various results of Ellentuck, Louveau, Mathias and Milliken concerning the extent ofC ℱ. We also study some cardinals that can be associated with the ideal ℐℱ of nowhere ℱ-Ramsey sets.
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  21.  5
    Partition Relations for Κ-Normal Ideals on Pκ.Pierre Matet - 2003 - Annals of Pure and Applied Logic 121 (1):89-111.
    Using previous work of Baumgartner, Shelah and others, we describe, for each infinite cardinal θκ, the smallest κ-normal ideal J on Pκ such that.
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  22.  11
    Scales with Various Kinds of Good Points.Pierre Matet - 2018 - Mathematical Logic Quarterly 64 (4-5):349-370.
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  23.  38
    Weak Square Bracket Relations for P Κ (Λ).Pierre Matet - 2008 - Journal of Symbolic Logic 73 (3):729-751.
    We study the partition relation $X@>{\rm w}>>[Y]_{p}^{2}$ that is a weakening of the usual partition relation $X\rightarrow [Y]_{p}^{2}$ . Our main result asserts that if κ is an uncountable strongly compact cardinal and $\germ{d}_{\kappa}\leq \lambda ^{<\kappa}$ , then $I_{\kappa,\lambda}^{+}@>{\rm w}>>[I_{\kappa,\lambda}^{+}]_{\lambda <\kappa}^{2}$ does not hold.
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  24.  13
    Weakly Normal Filters and the Closed Unbounded Filter on P Κ Λ Weakly Normal Filters and Large CardinalsWeakly Normal Ideals on  Κ Λ and the Singular Cardinal HypothesisSaturation of Fundamental Ideals on  Κ Λ Strongly Normal Ideals on  Κ Λ and the Sup-FunctionCombinatorics for Small Ideals on  Κ Λ Regularity of Ultrafilters and Fixed Points of Elementary Embeddings.Pierre Matet, Yoshihiro Abe & Masahiro Shioya - 2002 - Bulletin of Symbolic Logic 8 (2):309.
  25.  15
    A Generalization of the Dual Ellentuck Theorem.Lorenz Halbeisen & Pierre Matet - 2003 - Archive for Mathematical Logic 42 (2):103-128.
    We prove versions of the Dual Ramsey Theorem and the Dual Ellentuck Theorem for families of partitions which are defined in terms of games.
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  26.  9
    Guessing More Sets.Pierre Matet - 2015 - Annals of Pure and Applied Logic 166 (10):953-990.
  27.  8
    Some Coloring Properties for Uncountable Cardinals.Pierre Matet - 1987 - Annals of Pure and Applied Logic 33 (3):297-307.
  28.  4
    The Nonstationary Ideal on P_kappa for Lambda Singular.Pierre Matet & Saharon Shelah - 2017 - Archive for Mathematical Logic 56 (7-8):911-934.
    We give a new characterization of the nonstationary ideal on \\) in the case when \ is a regular uncountable cardinal and \ a singular strong limit cardinal of cofinality at least \.
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  29.  10
    [Omnibus Review].Pierre Matet - 2002 - Bulletin of Symbolic Logic 8 (2):309-311.
  30.  7
    Partition Relations for< I> Κ-Normal Ideals on< I> P_< Sub> Κ(< I> Λ).Pierre Matet - 2003 - Annals of Pure and Applied Logic 121 (1):89-111.
  31. REVIEWS-Seven Papers-PkM.Yoshihiro Abe & Pierre Matet - 2002 - Bulletin of Symbolic Logic 8 (2):309-311.
     
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