**Mathematical Surveys and Monographs**

Volume: 155;
2009;
502 pp;
Hardcover

MSC: Primary 03;
Secondary 28; 54

Print ISBN: 978-0-8218-4813-5

Product Code: SURV/155

List Price: $115.00

Individual Member Price: $92.00

**Electronic ISBN: 978-1-4704-1382-8
Product Code: SURV/155.E**

List Price: $115.00

Individual Member Price: $92.00

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#### Supplemental Materials

# Descriptive Set Theory: Second Edition

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*Yiannis N. Moschovakis*

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.

#### Table of Contents

# Table of Contents

## Descriptive Set Theory: Second Edition

- Contents vii9 free
- Preface to the Second Edition ix11 free
- Preface to the First Edition xi13 free
- About this Book xiii15 free
- Introduction 117 free
- Chapter 1. 925 free
- Chapter 2. $kappa$-Suslin and $lambda$-Borel 4965
- Chapter 3. Basic notions of the effective theory 87103
- Chapter 4. Structure theory for pointclasses 145161
- Chapter 5. The constructible universe 207223
- Chapter 6. The playful universe 217233
- Chapter 7. The recursion theorem 293309
- Chapter 8. Metamathematics 353369
- The Axiomatics of pointclasses 475491
- References 477493
- Index 491507 free

#### Readership

Graduate students and research mathematicians interested in set theory. especially descriptive set theory.

#### Reviews

The author added the most important references to the developments in descriptive set theory since 1980 when they touch questions formulated in the book.

-- Zentralblatt MATH