Classical Descriptive Set Theory
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Classical Descriptive Set Theory
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Author : Alexander Kechris
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Classical Descriptive Set Theory written by Alexander Kechris and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.
Descriptive Set Theory
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Author : Yiannis N. Moschovakis
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-06-30
Descriptive Set Theory written by Yiannis N. Moschovakis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-30 with Mathematics categories.
Descriptive Set Theory is the study of sets in separable, complete metric spaces that can be defined (or constructed), and so can be expected to have special properties not enjoyed by arbitrary pointsets. This subject was started by the French analysts at the turn of the 20th century, most prominently Lebesgue, and, initially, was concerned primarily with establishing regularity properties of Borel and Lebesgue measurable functions, and analytic, coanalytic, and projective sets. Its rapid development came to a halt in the late 1930s, primarily because it bumped against problems which were independent of classical axiomatic set theory. The field became very active again in the 1960s, with the introduction of strong set-theoretic hypotheses and methods from logic (especially recursion theory), which revolutionized it. This monograph develops Descriptive Set Theory systematically, from its classical roots to the modern ``effective'' theory and the consequences of strong (especially determinacy) hypotheses. The book emphasizes the foundations of the subject, and it sets the stage for the dramatic results (established since the 1980s) relating large cardinals and determinacy or allowing applications of Descriptive Set Theory to classical mathematics. The book includes all the necessary background from (advanced) set theory, logic and recursion theory.
Descriptive Set Theory And The Structure Of Sets Of Uniqueness
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Author : A. S. Kechris
language : en
Publisher: Cambridge University Press
Release Date : 1987-11-27
Descriptive Set Theory And The Structure Of Sets Of Uniqueness written by A. S. Kechris and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-11-27 with Mathematics categories.
To make this work accessible to logicians as well as set theorists and analysts, classical and modern theory of sets of uniqueness are covered as well as the relevant parts of descriptive set theory.
Invariant Descriptive Set Theory
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Author : Su Gao
language : en
Publisher: CRC Press
Release Date : 2008-09-03
Invariant Descriptive Set Theory written by Su Gao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-03 with Mathematics categories.
Presents Results from a Very Active Area of ResearchExploring an active area of mathematics that studies the complexity of equivalence relations and classification problems, Invariant Descriptive Set Theory presents an introduction to the basic concepts, methods, and results of this theory. It brings together techniques from various areas of mathem
Recursive Aspects Of Descriptive Set Theory
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Author : Richard Mansfield
language : en
Publisher: Oxford University Press, USA
Release Date : 1985
Recursive Aspects Of Descriptive Set Theory written by Richard Mansfield and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
Explores the nature of infinity with a view toward classifying and explaining its mathematical applications. It presents not only the basics of the classical theory, but also an introduction to the many important recent results and methods.
The Descriptive Set Theory Of Polish Group Actions
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Author : Howard Becker
language : en
Publisher: Cambridge University Press
Release Date : 1996-12-05
The Descriptive Set Theory Of Polish Group Actions written by Howard Becker and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-12-05 with Mathematics categories.
In this book the authors present their research into the foundations of the theory of Polish groups and the associated orbit equivalence relations. The particular case of locally compact groups has long been studied in many areas of mathematics. Non-locally compact Polish groups occur naturally as groups of symmetries in such areas as logic (especially model theory), ergodic theory, group representations, and operator algebras. Some of the topics covered here are: topological realizations of Borel measurable actions; universal actions; applications to invariant measures; actions of the infinite symmetric group in connection with model theory (logic actions); dichotomies for orbit spaces (including Silver, Glimm-Effros type dichotomies and the topological Vaught conjecture); descriptive complexity of orbit equivalence relations; definable cardinality of orbit spaces.
Descriptive Set Theoretic Methods In Automata Theory
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Author : Michał Skrzypczak
language : en
Publisher: Springer
Release Date : 2016-08-05
Descriptive Set Theoretic Methods In Automata Theory written by Michał Skrzypczak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-05 with Mathematics categories.
The book is based on the PhD thesis “Descriptive Set Theoretic Methods in Automata Theory,” awarded the E.W. Beth Prize in 2015 for outstanding dissertations in the fields of logic, language, and information. The thesis reveals unexpected connections between advanced concepts in logic, descriptive set theory, topology, and automata theory and provides many deep insights into the interplay between these fields. It opens new perspectives on central problems in the theory of automata on infinite words and trees and offers very impressive advances in this theory from the point of view of topology. "...the thesis of Michał Skrzypczak offers certainly what we expect from excellent mathematics: new unexpected connections between a priori distinct concepts, and proofs involving enlightening ideas.” Thomas Colcombet.
Invariant Descriptive Set Theory
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Author : Su Gao
language : en
Publisher: Chapman and Hall/CRC
Release Date : 2008-09-03
Invariant Descriptive Set Theory written by Su Gao and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-03 with Mathematics categories.
Presents Results from a Very Active Area of Research Exploring an active area of mathematics that studies the complexity of equivalence relations and classification problems, Invariant Descriptive Set Theory presents an introduction to the basic concepts, methods, and results of this theory. It brings together techniques from various areas of mathematics, such as algebra, topology, and logic, which have diverse applications to other fields. After reviewing classical and effective descriptive set theory, the text studies Polish groups and their actions. It then covers Borel reducibility results on Borel, orbit, and general definable equivalence relations. The author also provides proofs for numerous fundamental results, such as the Glimm–Effros dichotomy, the Burgess trichotomy theorem, and the Hjorth turbulence theorem. The next part describes connections with the countable model theory of infinitary logic, along with Scott analysis and the isomorphism relation on natural classes of countable models, such as graphs, trees, and groups. The book concludes with applications to classification problems and many benchmark equivalence relations. By illustrating the relevance of invariant descriptive set theory to other fields of mathematics, this self-contained book encourages readers to further explore this very active area of research.
Generalized Descriptive Set Theory And Classification Theory
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Author : Sy-David Friedman
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-06-05
Generalized Descriptive Set Theory And Classification Theory written by Sy-David Friedman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-05 with Mathematics categories.
Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper the authors study the generalization where countable is replaced by uncountable. They explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. They also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. The authors' results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.
Banach Spaces And Descriptive Set Theory Selected Topics
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Author : Pandelis Dodos
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-10
Banach Spaces And Descriptive Set Theory Selected Topics written by Pandelis Dodos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-10 with Mathematics categories.
This volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The novelty of the approach lies in the fact that the answers to a number of basic questions are based on techniques from Descriptive Set Theory. Although the book is oriented on proofs of several structural theorems, in the main text readers will also find a detailed exposition of numerous “intermediate” results which are interesting in their own right and have proven to be useful in other areas of Functional Analysis. Moreover, several well-known results in the geometry of Banach spaces are presented from a modern perspective.