Pierre Matet

Centre National de la Recherche Scientifique

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Saharon Shelah

Hebrew University of Jerusalem

Cédric Péan

Université de Caen Normandie

Andrzej Rosłanowski

University of Nebraska at Omaha

Laura Fontanella

Université Paris-Est Créteil

Toshimichi Usuba

Waseda University

Lorenz Halbeısen

ETH Zurich

Heike Mildenberger

University of Freiburg

Ulrich Kohlenbach

Technical University of Darmstadt

Massoud Pourmahdian

Amirkabir University of Technology

Stevo Todorčević

University of Toronto

Cooperative Institutions

Hebrew University of Jerusalem

University of Bonn

University of Wrocław

Centre National de la Recherche Scientifique

Université Paris Cité

Sorbonne Université

Institute of Mathematics

University of Freiburg

University of Vienna

Hebrew College

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Some filters of partitions

Journal of Symbolic Logic (1988)

Pierre Matet

§0. Introduction. We started our study of filters of partitions in [15]. We shall here restrict ourselves to the consideration of filters on (ω) ω , the set of all infinite partitions of ω. §1 is an attempt to elucidate the connection between filters on (ω) ω and filters over ω. Given a filter H over ω, we define two filters F H and G H on (ω) ω , and we characterize p -points, rare ultrafilters and Ramsey ultrafilters in terms of properties of the associated filters of partitions. The remainder of the paper is devoted to the study of those filters that can be associated with Hindman's theorem and its extensions. Let us introduce some notation. Suppose * is an associative operation on ω, and let a subset A of ω and an ordinal α with 0 < α ≤ ω be given.

Associative property

Chinese remainder theorem

10.2307/2274523

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Citations (10)

Concerning stationary subsets of [λ]<κ

Lecture notes in mathematics (1989)

Pierre Matet

10.1007/bfb0097335

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Citations (12)

Large cardinals and covering numbers

Fundamenta Mathematicae (2009)

Pierre Matet

The paper is concerned with the computation of covering numbers in the presence of large cardinals. In particular, we revisit Solovay's result that the Singular Cardinal Hypothesis holds above a strongly compact cardinal.

Regular cardinal

10.4064/fm205-1-3

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Weakly Normal Filters and the Closed Unbounded Filter on P κ λ</latex>

Bulletin of Symbolic Logic (2002)

Pierre Matet Yoshihiro Abe Masahiro Shioya

10.2307/2693975

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$μ$-Clubs OF $P_κ(λ)$ : Paradise on earth

arXiv (Cornell University) (2023)

Pierre Matet

If $V = L$, and $\mu$, $\kappa$ and $\lambda$ are three infinite cardinals with $\mu = {\rm cf} (\mu) < \kappa = {\rm cf}(\kappa) \leq \lambda$, then, as shown in \cite{Heaven}, the $\mu$-club filters on $P_\kappa (\lambda)$ and $P_\kappa (\lambda^{< \kappa})$ are isomorphic if and only if ${\rm cf} (\lambda) \not= \mu$. Now in $L$, $\lambda^{< \kappa}$ equals $u (\kappa, \lambda)$ (the least size of a cofinal subset in $(P_\kappa (\lambda), \subseteq)$) equals $\lambda$ if ${\rm cf} (\lambda) \geq \kappa$, and $\lambda^+$ otherwise. We show that, in ZFC, there are many triples $(\mu, \kappa, \lambda)$ for which ($u (\kappa, \lambda) > \lambda$ and) the $\mu$-club filters on $P_\kappa (\lambda)$ and $P_\kappa (u (\kappa, \lambda))$ are isomorphic.

Kappa

10.48550/arxiv.2308.14773

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Belegradek, O., Verbovskiy, V. and Wagner, FO, Coset

Joseph Y. Halpern Bruce M. Kapron Valentina Harizanov Ulrich Kohlenbach Paulo Oliva

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REVIEWS-Seven papers-PkM

Yoshihiro Abe Pierre Matet

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NEGATIVE PARTITION RELATIONS OR UNCOUNTABLE CARDINALS OF COFINALITY

Studia Scientiarum Mathematicarum Hungarica (2001)

Pierre Matet

We modify an argument of Baumgartner to show that…

Cofinality

Regular cardinal

10.1556/sscmath.37.2001.1-2.15

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Piece selection and cardinal arithmetic

arXiv (Cornell University) (2019)

Pierre Matet

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 $\lambda \geq 2^\kappa$, then (a) $I_{\kappa, \lambda}$ is not $(\lambda, 2)$-distributive, and (b) $I_{\kappa, \lambda}^+ \rightarrow (I_{\kappa, \lambda}^+)^2_\omega$ does not hold.

Kappa

Regular cardinal

10.48550/arxiv.1908.04375

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Positive partition relations for P_{kappa,lambda}

arXiv (Cornell University) (2004)

Pierre Matet Saharon Shelah

Let kappa a regular uncountable cardinal and lambda a cardinal >kappa, and suppose lambda^{^kappa (I_{kappa, lambda}^+,omega +1)^2, (b) I_{kappa, lambda}^+ -->^kappa [I_{kappa, lambda}^+]_{kappa^+}^2 if kappa is a limit cardinal, and (c) I_{kappa, lambda}^+ -->^kappa (I_{kappa, lambda}^+)^2 if kappa is weakly compact.

Kappa

Regular cardinal

10.48550/arxiv.math/0407440

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Citations (2)