**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

AMS Member Price: $92.00

MAA member Price: $103.50

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

List Price: $115.00

AMS Member Price: $92.00

MAA member Price: $103.50

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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.

#### Readership

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

#### Reviews & Endorsements

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

#### 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