Recursive Aspects Of Descriptive Set Theory PDF Download
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Author | : Richard Mansfield |
Publisher | : Oxford University Press, USA |
Total Pages | : 168 |
Release | : 1985 |
Genre | : Mathematics |
ISBN | : |
Download Recursive Aspects of Descriptive Set Theory Book in PDF, ePub and Kindle
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 | : Yiannis N. Moschovakis |
Publisher | : American Mathematical Soc. |
Total Pages | : 521 |
Release | : 2009-06-30 |
Genre | : Mathematics |
ISBN | : 0821848135 |
Download Descriptive Set Theory Book in PDF, ePub and Kindle
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 | : Alexander Kechris |
Publisher | : Springer Science & Business Media |
Total Pages | : 419 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461241901 |
Download Classical Descriptive Set Theory Book in PDF, ePub and Kindle
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 | : Su Gao |
Publisher | : CRC Press |
Total Pages | : 392 |
Release | : 2008-09-03 |
Genre | : Mathematics |
ISBN | : 9781584887942 |
Download Invariant Descriptive Set Theory Book in PDF, ePub and Kindle
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 | : A. S. Kechris |
Publisher | : Cambridge University Press |
Total Pages | : 384 |
Release | : 1987-11-27 |
Genre | : Mathematics |
ISBN | : 9780521358118 |
Download Descriptive Set Theory and the Structure of Sets of Uniqueness Book in PDF, ePub and Kindle
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 | : Arnold W. Miller |
Publisher | : Cambridge University Press |
Total Pages | : 135 |
Release | : 2017-05-18 |
Genre | : Mathematics |
ISBN | : 1107168066 |
Download Descriptive Set Theory and Forcing Book in PDF, ePub and Kindle
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 | : Howard Becker |
Publisher | : Cambridge University Press |
Total Pages | : 152 |
Release | : 1996-12-05 |
Genre | : Mathematics |
ISBN | : 0521576059 |
Download The Descriptive Set Theory of Polish Group Actions Book in PDF, ePub and Kindle
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 | : Chi Tat Chong |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 320 |
Release | : 2015-08-17 |
Genre | : Mathematics |
ISBN | : 311038129X |
Download Recursion Theory Book in PDF, ePub and Kindle
This monograph presents recursion theory from a generalized point of view centered on the computational aspects of definability. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using techniques and ideas from recursion theory, hyperarithmetic theory, and descriptive set theory. The emphasis is on the interplay between recursion theory and set theory, anchored on the notion of definability. The monograph covers a number of fundamental results in hyperarithmetic theory as well as some recent results on the structure theory of Turing and hyperdegrees. It also features a chapter on the applications of these investigations to higher randomness.
Author | : Gerald E. Sacks |
Publisher | : Cambridge University Press |
Total Pages | : 361 |
Release | : 2017-03-02 |
Genre | : Mathematics |
ISBN | : 1107168430 |
Download Higher Recursion Theory Book in PDF, ePub and Kindle
This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.
Author | : Herbert B. Enderton |
Publisher | : Academic Press |
Total Pages | : 294 |
Release | : 1977-05-23 |
Genre | : Mathematics |
ISBN | : 0080570429 |
Download Elements of Set Theory Book in PDF, ePub and Kindle
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.