Jech, Thomas. Review: Yiannis N. Moschovakis, Descriptive set theory. Bull. Amer. Math. Soc. (N.S.) 5 (), no. 3, This is a course covering the core material of descriptive set theory with a focus Y. Moschovakis: Descriptive set theory, American Mathematical Society In Descriptive Set Theory we try to avoid these pathologies by concentrating on natural While this is a restricted class of sets it includes most of the sets that arise naturally in Y. Moschovakis, Descriptive Set Theory, North-Holland,
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Mathematical Surveys and Monographs Volume: Descriptive Set Theory is the study of sets in separable, complete theoty spaces that can be defined or constructedand so can be expected to have special properties not moschpvakis 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 s, primarily because it bumped against problems which were moschovaiis of classical axiomatic set theory.
The field became very active again in the s, with the introduction of strong set-theoretic hypotheses and methods from logic especially recursion theorywhich revolutionized it.
The book emphasizes the foundations of the subject, and it sets the stage for the dramatic results established since the s 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.
Math Descriptive Set Theory
The author added the most important references to the developments in descriptive set theory since when they touch questions formulated in the book.
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