
Preface  Introduction  Table of Contents  Supplementary Material 
Mathematical Surveys and Monographs 2009; 502 pp; hardcover Volume: 155 ISBN10: 0821848135 ISBN13: 9780821848135 List Price: US$115 Member Price: US$92 Order Code: SURV/155 See also: Discovering Modern Set Theory. I: The Basics  Winfried Just and Martin Weese Discovering Modern Set Theory. II: SetTheoretic Tools for Every Mathematician  Winfried Just and Martin Weese  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 settheoretic 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 "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 


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