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Descriptive Theory Of Sets And Functions

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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 Theory Of Sets And Functions Functional Analysis In Semi Ordered Spaces

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Author : L.V. Kantorovich
language : en
Publisher: CRC Press
Release Date : 1996-02-19

Descriptive Theory Of Sets And Functions Functional Analysis In Semi Ordered Spaces written by L.V. Kantorovich and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-02-19 with Mathematics categories.

This book presents articles of L.V. Kantorovich on the descriptive theory of sets and function and on functional analysis in semi-ordered spaces, to demonstrate the unity of L.V. Kantorovich's creative research. It also includes two papers on the "extension of Hilbert space".

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 Theory Of Sets And Functions Functional Analysis In Semi Ordered Spaces

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Author : L.V. Kantorovich
language : en
Publisher: CRC Press
Release Date : 2024-12-11

Set Theory For The Working Mathematician

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Author : Krzysztof Ciesielski
language : en
Publisher: Cambridge University Press
Release Date : 1997-08-28

Set Theory For The Working Mathematician written by Krzysztof Ciesielski 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 1997-08-28 with Mathematics categories.

Presents those methods of modern set theory most applicable to other areas of pure mathematics.

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

Elements Of Set Theory

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Author : Herbert B. Enderton
language : en
Publisher: Gulf Professional Publishing
Release Date : 1977-04-28

Elements Of Set Theory written by Herbert B. Enderton and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-04-28 with Mathematics categories.

This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.

The Theory Of Cluster Sets

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Author : E. F. Collingwood
language : en
Publisher: Cambridge University Press
Release Date : 2004-06-03

The Theory Of Cluster Sets written by E. F. Collingwood 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 2004-06-03 with Mathematics categories.

An introduction to the theory of cluster sets, a branch of topological analysis.

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.

Descriptive Theory Of Sets And Functions Functional Analysis In Semi Ordered Spaces

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Author : L.V. Kantorovich
language : en
Publisher: CRC Press
Release Date : 1996-02-19

Descriptive Theory Of Sets And Functions

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