Descriptive set theory / Yiannis N. Moschovakis.

Format:

Book

Author/Creator:

Moschovakis, Yiannis N.

Series:

Studies in logic and the foundations of mathematics ; v. 100.

Studies in logic and the foundations of mathematics ; v. 100

Language:

English

Subjects (All):

Descriptive set theory.

Logic, Symbolic and mathematical.

Physical Description:

1 online resource (651 p.)

Place of Publication:

Amsterdam ; New York : North-Holland Pub. Co. ; New York : Sole distributors for the U.S.A. and Canada, Elsevier-North Holland, 1980.

Language Note:

English

Summary:

Now available in paperback, this monograph is a self-contained exposition of the main results and methods of descriptive set theory. It develops all the necessary background material from logic and recursion theory, and treats both classical descriptive set theory and the effective theory developed by logicians.

Contents:

Front Cover; Descriptive Set Theory; Copyright Page; Preface; Table of Contents; About This Book; Introduction; Chapter 1. The Basic Classical Notions; 1A. Perfect Polish spaces; 1B. The Borel pointclasses of finite order; 1C. Computing with relations; closure properties; 1D. Parametrization and hierarchy theorems; 1E. The projective sets; 1F. Countable operations and the transfinite Borel pointclasses; 1G. Borel functions and isomorphisms; 1H. Historical and other remarks; Chapter 2. x-Suslin and λ-Borel; 2A. The Cantor-Bendixson theorem; 2B. x-Suslin sets

2C. Trees and the perfect set theorem2D. Wellfounded trees; 2E. The Suslin theorem; 2F. Inductive analysis of projections of trees; 2G. The Kunen-Martin theorem; 2H. Category and measure; 2I. Historical remarks; Chapter 3. Basic Notions of the Effective Theory; 3A. Recursive functions on the integers; 3B. Recursive presentations; 3C. Semirecursive pointsets; 3D. Recursive and Γ-recursive functions; 3E. The Kleene pointclasses; 3F. Universal sets for the Kleene pointclasses; 3G. Partial functions and the substitution property; 3H. Codings, uniformity and good parametrizations

6C. The second periodicity theorem uniformization; 6D. The game quantifier G; 6E. The third periodicity theorem: definable winning strategies; 6F. The determinacy of Borel sets; 6G. Measurable cardinals; 6H. Historical remarks; Chafer 7. The Recursion Theorem; 7A . Recursion in a Σ*-pointclass; 7B. The Suslin-Kleene theorem; 7C. Inductive definability; 7D. The completely playful universe; 7E. Historical remarks; 7F. Appendix; a list of results which depend on the axiom of choice; Chapter 8. Metamathematics; 8A. Structures and languages; 8B. Elementary definability

8C. Definability in the universe of sets8D. Gödel's model of constructible sets; 8E. Absoluteness; 8F. The basic facts about L; 8G. Regularity results and inner models; 8H. On the theory of indiscernibles; 8I. Some remarks about strong hypotheses; 8J. Historical remarks; References and Index to References; Subject Index; Index of Symbols

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 613-622) and indexes.

ISBN:

1-282-28679-X

9786612286797

0-08-096319-6

OCLC:

499778252