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Author: Howard Becker
Publisher: Cambridge University Press
ISBN: 0521576059
Category : Mathematics
Languages : en
Pages : 152
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Book Description
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.
Author: Howard Becker
Publisher: Cambridge University Press
ISBN: 0521576059
Category : Mathematics
Languages : en
Pages : 152
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Book Description
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.
Author: Su Gao
Publisher: CRC Press
ISBN: 9781584887942
Category : Mathematics
Languages : en
Pages : 392
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Book Description
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
Author: Alexander Kechris
Publisher: Springer Science & Business Media
ISBN: 1461241901
Category : Mathematics
Languages : en
Pages : 419
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Book Description
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.
Author: Howard Becker
Publisher:
ISBN: 9781107367371
Category : Electronic books
Languages : en
Pages : 152
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Book Description
Research monograph on set theory by two of the world's leading researchers.
Author: A. S. Kechris
Publisher: American Mathematical Soc.
ISBN: 0821848941
Category : Mathematics
Languages : en
Pages : 258
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Book Description
A study of ergodic, measure preserving actions of countable discrete groups on standard probability spaces. It explores a direction that emphasizes a global point of view, concentrating on the structure of the space of measure preserving actions of a given group and its associated cocycle spaces.
Author: M. Foreman
Publisher: Cambridge University Press
ISBN: 9780521786447
Category : Mathematics
Languages : en
Pages : 304
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Book Description
This volume, first published in 2000, contains a collection of survey papers providing an introduction for graduate students and researchers in these fields.
Author: Paul B. Larson
Publisher: American Mathematical Soc.
ISBN: 1470454629
Category : Education
Languages : en
Pages : 330
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Book Description
This book introduces a new research direction in set theory: the study of models of set theory with respect to their extensional overlap or disagreement. In Part I, the method is applied to isolate new distinctions between Borel equivalence relations. Part II contains applications to independence results in Zermelo–Fraenkel set theory without Axiom of Choice. The method makes it possible to classify in great detail various paradoxical objects obtained using the Axiom of Choice; the classifying criterion is a ZF-provable implication between the existence of such objects. The book considers a broad spectrum of objects from analysis, algebra, and combinatorics: ultrafilters, Hamel bases, transcendence bases, colorings of Borel graphs, discontinuous homomorphisms between Polish groups, and many more. The topic is nearly inexhaustible in its variety, and many directions invite further investigation.
Author: Jan Van Eijck
Publisher: Cambridge University Press
ISBN: 1108583482
Category : Mathematics
Languages : en
Pages :
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Book Description
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the seventeenth publication in the Lecture Notes in Logic series, collects the proceedings of the European Summer Meeting of the Association for Symbolic Logic, held in Utrecht, The Netherlands in August, 1999. It includes surveys and research articles from some of the world's preeminent logicians. Two long articles are based on tutorials given at the meeting and present accessible expositions of current research in geometric model theory and the descriptive set theory of group actions. The other articles cover current research topics in all areas of mathematical logic, including proof theory, set theory, model theory, computability theory and philosophy.
Author: Sy-David Friedman
Publisher: American Mathematical Soc.
ISBN: 0821894757
Category : Mathematics
Languages : en
Pages : 80
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Book Description
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.
Author: Su Gao
Publisher: American Mathematical Soc.
ISBN: 0821831909
Category : Metric spaces
Languages : en
Pages : 78
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Book Description
