Classical 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.
Classical Descriptive Set Theory
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Author : Alexander Kechris
language : en
Publisher:
Release Date : 1995-01-06
Classical Descriptive Set Theory written by Alexander Kechris and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-06 with categories.
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
Banach Spaces And Descriptive Set Theory Selected Topics
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Author : Pandelis Dodos
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-10
Banach Spaces And Descriptive Set Theory Selected Topics written by Pandelis Dodos 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 2010-05-10 with Mathematics categories.
This volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The novelty of the approach lies in the fact that the answers to a number of basic questions are based on techniques from Descriptive Set Theory. Although the book is oriented on proofs of several structural theorems, in the main text readers will also find a detailed exposition of numerous “intermediate” results which are interesting in their own right and have proven to be useful in other areas of Functional Analysis. Moreover, several well-known results in the geometry of Banach spaces are presented from a modern perspective.
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.
Recursive Aspects Of Descriptive Set Theory
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Author : Richard Mansfield
language : en
Publisher: Oxford University Press, USA
Release Date : 1985
Recursive Aspects Of Descriptive Set Theory written by Richard Mansfield and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
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.
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.
A Course On Borel Sets
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Author : S.M. Srivastava
language : en
Publisher: Springer
Release Date : 2013-12-01
A Course On Borel Sets written by S.M. Srivastava and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
The roots of Borel sets go back to the work of Baire [8]. He was trying to come to grips with the abstract notion of a function introduced by Dirich let and Riemann. According to them, a function was to be an arbitrary correspondence between objects without giving any method or procedure by which the correspondence could be established. Since all the specific functions that one studied were determined by simple analytic expressions, Baire delineated those functions that can be constructed starting from con tinuous functions and iterating the operation 0/ pointwise limit on a se quence 0/ functions. These functions are now known as Baire functions. Lebesgue [65] and Borel [19] continued this work. In [19], Borel sets were defined for the first time. In his paper, Lebesgue made a systematic study of Baire functions and introduced many tools and techniques that are used even today. Among other results, he showed that Borel functions coincide with Baire functions. The study of Borel sets got an impetus from an error in Lebesgue's paper, which was spotted by Souslin. Lebesgue was trying to prove the following: Suppose / : )R2 -- R is a Baire function such that for every x, the equation /(x,y) = 0 has a. unique solution. Then y as a function 0/ x defined by the above equation is Baire.