37 found
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  1.  61
    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.  11
    Scales with various kinds of good points.Pierre Matet - 2018 - Mathematical Logic Quarterly 64 (4-5):349-370.
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  3.  27
    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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  4.  12
    Guessing more sets.Pierre Matet - 2015 - Annals of Pure and Applied Logic 166 (10):953-990.
  5.  11
    When P(λ) (vaguely) resembles κ.Pierre Matet - 2021 - Annals of Pure and Applied Logic 172 (2):102874.
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  6.  4
    Two-cardinal diamond star.Pierre Matet - 2014 - Mathematical Logic Quarterly 60 (4-5):246-265.
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  7.  4
    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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  8.  9
    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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  9.  21
    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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  10.  2
    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, and a cardinal greater than or equal to $\kappa $. Revisiting a celebrated result of Shelah, we show that if is close to $\kappa $ and (= the least size of a cofinal subset of ) is greater than, then can 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 if and, then no (...)
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  11.  52
    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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  12.  23
    Some Aspects ofn-Subtlety.Pierre Matet - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (2):189-192.
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  13.  8
    Two-cardinal versions of weak compactness: Partitions of pairs.Pierre Matet & Toshimichi Usuba - 2012 - Annals of Pure and Applied Logic 163 (1):1-22.
  14. 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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  15.  15
    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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  16.  50
    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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  17.  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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  18.  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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  19.  18
    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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  20.  19
    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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  21.  18
    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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  22.  3
    Some Aspects of n‐Subtlety.Pierre Matet - 1988 - Mathematical Logic Quarterly 34 (2):189-192.
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  23.  16
    Some filters of partitions.Pierre Matet - 1988 - Journal of Symbolic Logic 53 (2):540-553.
  24.  21
    Yoshihiro Abe. Weakly normal filters and the closed unbounded filter on P k λ_. Proceedings of the American Mathematical Society, vol. 104 (1998), pp. 1226–1234. - Yoshihiro Abe. _Weakly normal filters and large cardinals_. Tsukuba journal of mathematics, vol. 16 (1992), pp. 487–494. - Yoshihiro Abe. _Weakly normal ideals on P k λ and the singular cardinal hypothesis_. Fundamenta mathematicae, vol. 143 (1993), pp. 97–106. - Yoshihiro Abe. _Saturation of fundamental ideals on P k λ_. Journal of the Mathematical Society of Japan, vol. 48 (1996), pp. 511–524. - Yoshihiro Abe. _Strongly normal ideals on P k λ and the Sup-function_. opology and its applications, vol. 74 (1996), pp. 97–107. - Yoshihiro Abe. _Combinatorics for small ideals on P k λ_. Mathematical logic quarterly, vol. 43 (1997), pp. 541–549. - Yoshihiro Abe and Masahiro Shioya. _Regularity of ultrafilters and fixed points of elementary embeddings. Tsukuba journal of mathematics, vol. 22 (1998), pp. 31–37. [REVIEW]Pierre Matet - 2002 - Bulletin of Symbolic Logic 8 (2):309-311.
  25. REVIEWS-Seven papers-PkM.Yoshihiro Abe & Pierre Matet - 2002 - Bulletin of Symbolic Logic 8 (2):309-311.
     
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  26. Regularity of Ultrafilters and Fixed Points of Elementary Embeddings.Pierre Matet, Yoshihiro Abe & Masahiro Shioya - 2002 - Bulletin of Symbolic Logic 8 (2):309.
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  27.  8
    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.
  28.  44
    Weak square bracket relations for P κ (λ).Pierre Matet - 2008 - Journal of Symbolic Logic 73 (3):729-751.
    We study the partition relation [email protected]>{\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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  29.  15
    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.
  30.  16
    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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  31.  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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  32.  9
    Some coloring properties for uncountable cardinals.Pierre Matet - 1987 - Annals of Pure and Applied Logic 33 (C):297-307.
  33.  1
    Piece selection and cardinal arithmetic.Pierre Matet - 2022 - Mathematical Logic Quarterly 68 (4):416-446.
    We study the effects of piece selection principles on cardinal arithmetic (Shelah style). As an application, we discuss questions of Abe and Usuba. In particular, we show that if λ ≥ 2 κ $\lambda \ge 2^\kappa$, then (a) I κ, λ $I_{\kappa, \lambda }$ is not (λ, 2)-distributive, and (b) I κ, λ + → ( I κ, λ + ) ω 2 $I_{\kappa, \lambda }^+ \rightarrow (I_{\kappa, \lambda }^+)^2_\omega$ does not hold.
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  34.  11
    [Omnibus Review].Pierre Matet - 2002 - Bulletin of Symbolic Logic 8 (2):309-311.
  35.  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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  36.  1
    The secret life of μ-clubs.Pierre Matet - 2022 - Annals of Pure and Applied Logic 173 (9):103162.
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  37. 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 σ + 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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