Descriptive Set Theory
by Yiannis N. Moschovakis
Publisher: American Mathematical Society 2009
Number of pages: 516
Descriptive Set Theory is the study of sets in separable, complete metric spaces that can be defined, and so can be expected to have special properties not enjoyed by arbitrary pointsets. This monograph develops Descriptive Set Theory systematically, from its classical roots to the modern "effective" theory and the consequences of strong hypotheses. The book emphasizes the foundations of the subject, and it sets the stage for the dramatic results relating large cardinals and determinacy or allowing applications of Descriptive Set Theory to classical mathematics.
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by A. C. Walczak-Typke
From the table of contents: Learning to Speak; The Axioms of Set Theory; Orders and Ordinals; Cardinal Numbers; The Axiom of Regularity; Some Consistency Results; Goedel's Constructible Universe L; Independence of AC from ZFU; Forcing.
by Curtis T. McMullen - Harvard University
Introduction to conceptual and axiomatic mathematics, the writing of proofs, mathematical culture, with sets, groups and knots as topics. From the table of contents: Introduction; Set Theory; Group Theory; Knot Theory; Summary.
by David Marker - University of Illinois at Chicago
These are informal notes for a course in Descriptive Set Theory. While I hope to give a fairly broad survey of the subject we will be concentrating on problems about group actions, particularly those motivated by Vaught's conjecture.
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Introduction to the set theoretic tools for anyone who comes into contact with modern Mathematics. The intended audience are students of any subject or practitioners who need some knowledge of set operations and related topics.