Eliot Benoit (25 results)
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- Softcover
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- Softcover
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- Softcover
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- Softcover
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- Softcover
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- Hardcover
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- Softcover
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- Softcover
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- Hardcover
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Milliken's Tree Theorem and Its Applications: a Computability-Theoretic Perspective
Paul-Elliot Angles D'Auriac, Peter A. Cholak, Damir D. Dzhafarov, Benoit Monin, Ludovic Patey
- Softcover
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Paperback. Condition: New. Milliken's tree theorem is a deep result in combinatorics that generalizes a vast number of other results in the subject, most notably Ramsey's theorem and its many variants and consequences. In this sense, Milliken's tree theorem is paradigmatic of structural Ramsey theory, which seeks to identify the… common combinatorial and logical features of partition results in general. Its investigation in this area has consequently been extensive.Motivated by a question of Dobrinen, we initiate the study of Milliken's tree theorem from the point of view of computability theory. The goal is to understand how close it is to being algorithmically solvable, and how computationally complex are the constructions needed to prove it. This kind of examination enjoys a long and rich history, and continues to be a highly active endeavor. Applied to combinatorial principles, particularly Ramsey's theorem, it constitutes one of the most fruitful research programs in computability theory as a whole. The challenge to studying Milliken's tree theorem using this framework is its unusually intricate proof, and more specifically, the proof of the Halpern-La¨uchli theorem, which is a key ingredient.Our advance here stems from a careful analysis of the Halpern-Läuchli theorem which shows that it can be carried out effectively (i.e., that it is computably true). We use this as the basis of a new inductive proof of Milliken's tree theorem that permits us to gauge its effectivity in turn. The key combinatorial tool we develop for the inductive step is a fast-growing computable function that can be used to obtain a finitary, or localized, version of Milliken's tree theorem. This enables us to build solutions to the full Milliken's tree theorem using effective forcing. The principal result of this is a full classification of the computable content of Milliken's tree theorem in terms of the jump hierarchy, stratified by the size of instance. As usual, this also translates into the parlance of reverse mathematics, yielding a complete understanding of the fragment of second-order arithmetic required to prove Milliken's tree theorem.We apply our analysis also to several well-known applications of Milliken's tree theorem, namely Devlin's theorem, a partition theorem for Rado graphs, and a generalized version of the so-called tree theorem of Chubb, Hirst, and McNicholl. These are all certain kinds of extensions of Ramsey's theorem for different structures, namely the rational numbers, the Rado graph, and perfect binary trees, respectively. We obtain a number of new results about how these principles relate to Milliken's tree theorem and to each other, in terms of both their computability-theoretic and combinatorial aspects. In particular, we establish new structural Ramsey-theoretic properties of the Rado graph theorem and the generalized Chubb-Hirst-McNicholl tree theorem using Zucker's notion of big Ramsey structure.
Milliken's Tree Theorem and Its Applications: A Computability-Theoretic Perspective: Volume: 293 Number: 1457 (Memoirs of the American Mathematical Society)
D'Auriac, Paul-Elliot Angles/ Cholak, Peter A./ Dzhafarov, Damir D./ Monin, Benoit/ Patey, Ludovic
- Softcover
Seller: Revaluation Books, Exeter, United KingdomRevaluation Books
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Milliken's Tree Theorem and Its Applications: a Computability-Theoretic Perspective
Paul-Elliot Angles D'Auriac, Peter A. Cholak, Damir D. Dzhafarov, Benoit Monin, Ludovic Patey
- Softcover
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Paperback. Condition: New. Milliken's tree theorem is a deep result in combinatorics that generalizes a vast number of other results in the subject, most notably Ramsey's theorem and its many variants and consequences. In this sense, Milliken's tree theorem is paradigmatic of structural Ramsey theory, which seeks to identify the… common combinatorial and logical features of partition results in general. Its investigation in this area has consequently been extensive.Motivated by a question of Dobrinen, we initiate the study of Milliken's tree theorem from the point of view of computability theory. The goal is to understand how close it is to being algorithmically solvable, and how computationally complex are the constructions needed to prove it. This kind of examination enjoys a long and rich history, and continues to be a highly active endeavor. Applied to combinatorial principles, particularly Ramsey's theorem, it constitutes one of the most fruitful research programs in computability theory as a whole. The challenge to studying Milliken's tree theorem using this framework is its unusually intricate proof, and more specifically, the proof of the Halpern-La¨uchli theorem, which is a key ingredient.Our advance here stems from a careful analysis of the Halpern-Läuchli theorem which shows that it can be carried out effectively (i.e., that it is computably true). We use this as the basis of a new inductive proof of Milliken's tree theorem that permits us to gauge its effectivity in turn. The key combinatorial tool we develop for the inductive step is a fast-growing computable function that can be used to obtain a finitary, or localized, version of Milliken's tree theorem. This enables us to build solutions to the full Milliken's tree theorem using effective forcing. The principal result of this is a full classification of the computable content of Milliken's tree theorem in terms of the jump hierarchy, stratified by the size of instance. As usual, this also translates into the parlance of reverse mathematics, yielding a complete understanding of the fragment of second-order arithmetic required to prove Milliken's tree theorem.We apply our analysis also to several well-known applications of Milliken's tree theorem, namely Devlin's theorem, a partition theorem for Rado graphs, and a generalized version of the so-called tree theorem of Chubb, Hirst, and McNicholl. These are all certain kinds of extensions of Ramsey's theorem for different structures, namely the rational numbers, the Rado graph, and perfect binary trees, respectively. We obtain a number of new results about how these principles relate to Milliken's tree theorem and to each other, in terms of both their computability-theoretic and combinatorial aspects. In particular, we establish new structural Ramsey-theoretic properties of the Rado graph theorem and the generalized Chubb-Hirst-McNicholl tree theorem using Zucker's notion of big Ramsey structure.
- Softcover
Seller: RECYCLIVRE, Paris, FranceRECYCLIVRE
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- Softcover
Seller: RECYCLIVRE, Paris, FranceRECYCLIVRE
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Condition: Bon. Attention: Ancien support de bibliothèque, plastifié, étiquettes. Merci, votre achat aide à financer des programmes de lutte contre l'illettrisme.
PHOTOGRAPHIER EN NORMANDIE 1840-1890: UN DIALOGUE PIONNIER ENTRE LES ARTS
DELAPIERRE, EMMANUELLE; ROUET, DOMINIQUE; Aubenas, Sylvie; ELIOT, BENOÎT
- Hardcover
Seller: Gallix, Gif sur Yvette, FranceGallix
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Condition: Neuf.
Language: French
Published by Point De Vues, Bibliothèque Municipale De Rouen, 2001
- Softcover
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Language: French
Published by Point De Vues, Bibliothèque Municipale De Rouen, 2001
- Softcover
Seller: RECYCLIVRE, Paris, FranceRECYCLIVRE
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- Softcover
Seller: Buchpark, Trebbin, GermanyBuchpark
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Condition: Hervorragend. Zustand: Hervorragend | Seiten: 80 | Sprache: Französisch | Produktart: Bücher | Keine Beschreibung verfügbar.
Une Campagne Photographique dans l'Eure au temps de l'Impressionisme. Écho contemporain avec Daniel Quesney.
ELIOT Benoit - Stéphane RIOLAND ( conception éditoriale ) - [ ] Daniel QUESNEY - Jules CAMUS ( photographe ) - Département de l'EURE - ÉVREUX :
- Softcover
Seller: Antiquariaat Wim de Goeij, Kalmthout, ANTW, BelgiumAntiquariaat Wim de Goeij
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Add to basketÉvreux, éditions Point de Vue, 2010, in-4°, 288 pp, broché, couverture souple d'origine. Publié à l'occasion d'une exposition. L'Oeuvre photographique de Jules Camus ( 19e siècle) dans le département de l'Eure. ISBN 9782915548495 .
Published by 1991, 1991
Seller: ChouetteCoop, Kervignac, FranceChouetteCoop
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Condition: Used: Good. Occasion - Bon Etat - En ville (1991) - Grand Format.
- Softcover
- Print on Demand
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
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Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - A collection of poems that I scribbled. I usually write after someone has made me cry so. 21 times someone made me cry and what came out of it.
- Softcover
- Print on Demand
Seller: preigu, Osnabrück, Germanypreigu
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Taschenbuch. Condition: Neu. Nobody's Son, Nobody's Daughter | Flynn-Elliot Benoit | Taschenbuch | Englisch | 2023 | Libresco Feeds Private Limited | EAN 9789357614962 | Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, 36244 Bad Hersfeld, gpsr[at]libri[dot]de | Anbieter: preigu Print on Demand.
