An error was encountered while trying to add the item to the cart. Please try again.
Copy To Clipboard
Successfully Copied!
Descriptive Set Theory: Second Edition

Yiannis N. Moschovakis University of California, Los Angeles, Los Angeles, CA and University of Athens, Athens, Greece
Available Formats:
Hardcover ISBN: 978-0-8218-4813-5
Product Code: SURV/155
List Price: $122.00 MAA Member Price:$109.80
AMS Member Price: $97.60 Electronic ISBN: 978-1-4704-1382-8 Product Code: SURV/155.E List Price:$115.00
MAA Member Price: $103.50 AMS Member Price:$92.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $183.00 MAA Member Price:$164.70
AMS Member Price: $146.40 Click above image for expanded view Descriptive Set Theory: Second Edition Yiannis N. Moschovakis University of California, Los Angeles, Los Angeles, CA and University of Athens, Athens, Greece Available Formats:  Hardcover ISBN: 978-0-8218-4813-5 Product Code: SURV/155  List Price:$122.00 MAA Member Price: $109.80 AMS Member Price:$97.60
 Electronic ISBN: 978-1-4704-1382-8 Product Code: SURV/155.E
 List Price: $115.00 MAA Member Price:$103.50 AMS Member Price: $92.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$183.00 MAA Member Price: $164.70 AMS Member Price:$146.40
• Book Details

Mathematical Surveys and Monographs
Volume: 1552009; 502 pp
MSC: Primary 03; Secondary 28; 54;

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.

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

• Chapters
• 1. Introduction
• 2. The basic classical notions
• 3. $\kappa$-Suslin and $\lambda$-Borel
• 4. Basic notions of the effective theory
• 5. Structure theory for pointclasses
• 6. The constructible universe
• 7. The playful universe
• 8. The recursion theorem
• 9. Metamathematics

• 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1552009; 502 pp
MSC: Primary 03; Secondary 28; 54;

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.

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

• Chapters
• 1. Introduction
• 2. The basic classical notions
• 3. $\kappa$-Suslin and $\lambda$-Borel
• 4. Basic notions of the effective theory
• 5. Structure theory for pointclasses
• 6. The constructible universe
• 7. The playful universe
• 8. The recursion theorem
• 9. Metamathematics
• 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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
You may be interested in...
Please select which format for which you are requesting permissions.