Invariant Descriptive Set Theory

Author : Su Gao
Publisher : CRC Press
ISBN 13 : 9781584887942
Total Pages : 392 pages
Book Rating : 4.4X/5 ( download)

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Download or read book Invariant Descriptive Set Theory written by Su Gao and published by CRC Press. This book was released on 2008-09-03 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Yiannis N. Moschovakis
Publisher : American Mathematical Soc.
ISBN 13 : 0821848135
Total Pages : 521 pages
Book Rating : 4.35/5 ( download)

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Download or read book Descriptive Set Theory written by Yiannis N. Moschovakis and published by American Mathematical Soc.. This book was released on 2009-06-30 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Richard Mansfield
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 168 pages
Book Rating : 4.45/5 ( download)

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Download or read book Recursive Aspects of Descriptive Set Theory written by Richard Mansfield and published by Oxford University Press, USA. This book was released on 1985 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : A. S. Kechris
Publisher : Cambridge University Press
ISBN 13 : 9780521358118
Total Pages : 384 pages
Book Rating : 4.16/5 ( download)

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Download or read book Descriptive Set Theory and the Structure of Sets of Uniqueness written by A. S. Kechris and published by Cambridge University Press. This book was released on 1987-11-27 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Alexander Kechris
Publisher : Springer Science & Business Media
ISBN 13 : 1461241901
Total Pages : 419 pages
Book Rating : 4.04/5 ( download)

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Download or read book Classical Descriptive Set Theory written by Alexander Kechris and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Cambridge University Press
ISBN 13 : 0521576059
Total Pages : 152 pages
Book Rating : 4.55/5 ( download)

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Download or read book The Descriptive Set Theory of Polish Group Actions written by Howard Becker and published by Cambridge University Press. This book was released on 1996-12-05 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Douglas Edward Miller
Publisher :
ISBN 13 :
Total Pages : 304 pages
Book Rating : 4.23/5 ( download)

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Download or read book Invariant Descriptive Set Theory and the Topological Approach to Model Theory written by Douglas Edward Miller and published by . This book was released on 1976 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Jindřich Zapletal
Publisher : American Mathematical Soc.
ISBN 13 : 0821834509
Total Pages : 158 pages
Book Rating : 4.03/5 ( download)

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Download or read book Descriptive Set Theory and Definable Forcing written by Jindřich Zapletal and published by American Mathematical Soc.. This book was released on 2004 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on the relationship between definable forcing and descriptive set theory; the forcing serves as a tool for proving independence of inequalities between cardinal invariants of the continuum.

Author : Sy-David Friedman
Publisher : American Mathematical Soc.
ISBN 13 : 0821894757
Total Pages : 92 pages
Book Rating : 4.50/5 ( download)

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Download or read book Generalized Descriptive Set Theory and Classification Theory written by Sy-David Friedman and published by American Mathematical Soc.. This book was released on 2014-06-05 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : J. Barwise
Publisher : Cambridge University Press
ISBN 13 : 1316739392
Total Pages : 913 pages
Book Rating : 4.96/5 ( download)

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Download or read book Model-Theoretic Logics written by J. Barwise and published by Cambridge University Press. This book was released on 2017-03-02 with total page 913 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 eighth publication in the Perspectives in Logic series, brings together several directions of work in model theory between the late 1950s and early 1980s. It contains expository papers by pre-eminent researchers. Part I provides an introduction to the subject as a whole, as well as to the basic theory and examples. The rest of the book addresses finitary languages with additional quantifiers, infinitary languages, second-order logic, logics of topology and analysis, and advanced topics in abstract model theory. Many chapters can be read independently.