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 attempts to present a largely balanced approach, which combines many elements of the different traditions of the subject. It includes a wide variety of examples, exercises (over 400), and applications, in order to illustrate the general concepts and results of the theory. This text provides a first basic course in classical descriptive set theory and covers material with which mathematicians interested in the subject for its own sake or those that wish to use it in their field should be familiar. Over the years, researchers in diverse areas of mathematics, such as logic and set theory, analysis, topology, probability theory, etc., have brought to the subject of descriptive set theory their own intuitions, concepts, terminology and notation.
Descriptive Set Theory
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Author : Yiannis N. Moschovakis
language : en
Publisher: American Mathematical Society
Release Date : 2025-01-31
Descriptive Set Theory written by Yiannis N. Moschovakis and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-31 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 Forcing
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Author : Arnold W. Miller
language : en
Publisher:
Release Date : 2002-01-01
Descriptive Set Theory And Forcing written by Arnold W. Miller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Borel sets categories.
This text is based on a graduate course given by the author at the University of Wisconsin. It presents an exposition of basic material from descriptive set theory (the general theory of Borel sets and projective sets), leading up to a new proof of Louveau's separation theorem for analytic sets. It assumes some background in mathematical logic and set theory, and should be of interest to reseachers and advanced students in these areas as well as in mathematical analysis. 4
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
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.
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.
Generalized Descriptive Set Theory And Classification Theory
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Author : Sy D. Friedman
language : en
Publisher:
Release Date : 2014-10-03
Generalized Descriptive Set Theory And Classification Theory written by Sy D. Friedman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-03 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.
Descriptive Set Theory
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Author : Yiannis N. Moschovakis
language : en
Publisher:
Release Date : 2014-05-21
Descriptive Set Theory written by Yiannis N. Moschovakis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-21 with MATHEMATICS categories.
Descriptive Set Theory And Definable Forcing
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Author : Jindřich Zapletal
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Descriptive Set Theory And Definable Forcing written by Jindřich Zapletal 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 2004 with Mathematics categories.
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.
Descriptive Set Theory And Forcing
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Author : Arnold W. Miller
language : en
Publisher: Cambridge University Press
Release Date : 2017-05-18
Descriptive Set Theory And Forcing written by Arnold W. Miller 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 2017-05-18 with Mathematics categories.
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.