Paul elliot angles dauriac (6 risultati)
- Brossura
Da: PBShop.store UK, Fairford, GLOS, Regno UnitoPBShop.store UK
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 79,69
EUR 3,84 spedizioneSpedito da Regno Unito a U.S.A.Quantità: 4 disponibili
PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000.
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
- Brossura
Da: Rarewaves.com USA, London, LONDO, Regno UnitoRarewaves.com USA
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 83,84
Spedizione gratuitaSpedito da Regno Unito a U.S.A.Quantità: 2 disponibili
Paperback. Condizione: 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 th…e 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
- Brossura
Da: Revaluation Books, Exeter, Regno UnitoRevaluation Books
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 88,74
EUR 11,66 spedizioneSpedito da Regno Unito a U.S.A.Quantità: 2 disponibili
Paperback. Condizione: Brand New. 118 pages. In Stock.
Milliken's Tree Theorem and Its Applications: a Computability-Theoretic Perspective (Memoirs of the American Mathematical Society)
D'Auriac Paul-Elliot, Angles, A. Cholak Peter D. Dzhafarov Damir u. a.:
- Brossura
Da: Studibuch, Stuttgart, GermaniaStudibuch
Contatta il venditoreVenditore con 5 stelleCondizione: Usato - Ottimo
EUR 32,57
EUR 80,70 spedizioneSpedito da Germania a U.S.A.Quantità: 1 disponibili
paperback. Condizione: Sehr gut. 118 Seiten; 9781470467319.2 Gewicht in Gramm: 500.
- Brossura
Da: THE SAINT BOOKSTORE, Southport, Regno UnitoTHE SAINT BOOKSTORE
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 101,08
EUR 15,71 spedizioneSpedito da Regno Unito a U.S.A.Quantità: 4 disponibili
Paperback / softback. Condizione: New. New copy - Usually dispatched within 4 working days.
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
- Brossura
Da: Rarewaves.com UK, London, Regno UnitoRarewaves.com UK
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 81,29
EUR 75,80 spedizioneSpedito da Regno Unito a U.S.A.Quantità: 2 disponibili
Paperback. Condizione: 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 th…e 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.
