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Author : Douglas Edward Miller
Publisher :
ISBN 13 :
Total Pages : 304 pages
Book Rating : 4.:/5 (34 download)
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 : Su Gao
Publisher : Chapman and Hall/CRC
ISBN 13 : 9781584887935
Total Pages : 0 pages
Book Rating : 4.8/5 (879 download)
Download or read book Invariant Descriptive Set Theory written by Su Gao and published by Chapman and Hall/CRC. This book was released on 2008-09-03 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Jörg Flum
Publisher : Springer
ISBN 13 : 3540385444
Total Pages : 161 pages
Book Rating : 4.5/5 (43 download)
Download or read book Topological Model Theory written by Jörg Flum and published by Springer. This book was released on 2006-11-14 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. S. Kechris
Publisher : Cambridge University Press
ISBN 13 : 9780521358118
Total Pages : 384 pages
Book Rating : 4.3/5 (581 download)
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 : Kazimierz Kuratowski
Publisher : Elsevier
ISBN 13 : 1483151638
Total Pages : 353 pages
Book Rating : 4.4/5 (831 download)
Download or read book Introduction to Set Theory and Topology written by Kazimierz Kuratowski and published by Elsevier. This book was released on 2014-07-10 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered. This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its application to propositions each having one of two logical values, 0 and 1. Operations on sets which are analogous to arithmetic operations are also discussed. The chapters that follow focus on the mapping concept, the power of a set, operations on cardinal numbers, order relations, and well ordering. The section on topology explores metric and topological spaces, continuous mappings, cartesian products, and other spaces such as spaces with a countable base, complete spaces, compact spaces, and connected spaces. The concept of dimension, simplexes and their properties, and cuttings of the plane are also analyzed. This book is intended for students and teachers of mathematics.
Author : Su Gao
Publisher : CRC Press
ISBN 13 : 9781584887942
Total Pages : 392 pages
Book Rating : 4.8/5 (879 download)
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 : Berd Van Der Steeg
Publisher : Delft University Press
ISBN 13 : 9789040724190
Total Pages : 125 pages
Book Rating : 4.7/5 (241 download)
Download or read book Models in Topology written by Berd Van Der Steeg and published by Delft University Press. This book was released on 2003-01-01 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Transitive sets of functions, A new cardinal invariant, A model theoretic approach to continuum theory, Model-theoretic continuum theory, Base-free properties, Span and chainability, chainability and span in the lattice language, On a theorem of Mackowiak and Tymchatyn, Two main lemmas, More old theorems and new proofs, On a theorem of Van Hartskamp and Vermeer, Model theory, Compactness and completeness."
Author : Cyrus F. Nourani
Publisher : CRC Press
ISBN 13 : 1482231506
Total Pages : 296 pages
Book Rating : 4.4/5 (822 download)
Download or read book A Functorial Model Theory written by Cyrus F. Nourani and published by CRC Press. This book was released on 2016-04-19 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to a functorial model theory based on infinitary language categories. The author introduces the properties and foundation of these categories before developing a model theory for functors starting with a countable fragment of an infinitary language. He also presents a new technique for generating generic models with categories by inventing infinite language categories and functorial model theory. In addition, the book covers string models, limit models, and functorial models.
Author : Jindřich Zapletal
Publisher : American Mathematical Soc.
ISBN 13 : 0821834509
Total Pages : 158 pages
Book Rating : 4.8/5 (218 download)
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 :
Publisher :
ISBN 13 :
Total Pages : 816 pages
Book Rating : 4.3/5 (91 download)
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1989 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Author : Sy-David Friedman
Publisher : American Mathematical Soc.
ISBN 13 : 0821894757
Total Pages : 92 pages
Book Rating : 4.8/5 (218 download)
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 : Lev D. Beklemishev
Publisher : Elsevier
ISBN 13 : 0080954952
Total Pages : 529 pages
Book Rating : 4.0/5 (89 download)
Download or read book SET THEORY written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: SET THEORY
Author : Arnold W. Miller
Publisher : Cambridge University Press
ISBN 13 : 1316739317
Total Pages : 136 pages
Book Rating : 4.3/5 (167 download)
Download or read book Descriptive Set Theory and Forcing written by Arnold W. Miller and published by Cambridge University Press. This book was released on 2017-05-18 with total page 136 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. In this volume, the fourth publication in the Lecture Notes in Logic series, Miller develops the necessary features of the theory of descriptive sets in order to present a new proof of Louveau's separation theorem for analytic sets. While some background in mathematical logic and set theory is assumed, the material is based on a graduate course given by the author at the University of Wisconsin, Madison, and is thus accessible to students and researchers alike in these areas, as well as in mathematical analysis.
Author : Yiannis N. Moschovakis
Publisher : American Mathematical Soc.
ISBN 13 : 0821848135
Total Pages : 521 pages
Book Rating : 4.8/5 (218 download)
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 : Kazimierz Kuratowski
Publisher :
ISBN 13 :
Total Pages : 514 pages
Book Rating : 4.:/5 (488 download)
Download or read book Set Theory written by Kazimierz Kuratowski and published by . This book was released on 1976 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Arnold W. Miller
Publisher : Cambridge University Press
ISBN 13 : 1107168066
Total Pages : 135 pages
Book Rating : 4.1/5 (71 download)
Download or read book Descriptive Set Theory and Forcing written by Arnold W. Miller and published by Cambridge University Press. This book was released on 2017-05-18 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes develop the theory of descriptive sets, leading up to a new proof of Louveau's separation theorem for analytic sets. A first course in mathematical logic and set theory is assumed, making this book suitable for advanced students and researchers.
Author :
Publisher :
ISBN 13 :
Total Pages : 504 pages
Book Rating : 4.3/5 ( download)
Download or read book Fundamenta Mathematicae written by and published by . This book was released on 1983 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt:
