Effective descriptive set theory is the study of definable sets of natural and real numbers, or, more generally Polish (separable, complete, metrizable) spaces. It extends and refines the classical theory of Borel, analytic and projective sets in Polish spaces using methods from recursion theory, and in some cases it provides new proofs and new results in the classical theory.

The aim of this course is to introduce the basic notions, methods, facts and applications of effective descriptive set theory : there will be no attempt to cover the subject in a comprehensive way.

This class is aimed at fairly advanced graduate students in logic, who know basic recursion theory (at least through the arithmetical hierarchy); set theory (including transfinite recursion); basic analysis and (metric) topology; and certainly logic. (All but the topology bit of this material is covered in Mathematics 220ABC.) No classical descriptive set theory will be assumed, but in some cases we may refer to more advanced material from set theory (e.g., measurable cardinals and determinacy hypotheses).

The course will be taught from notes which will be posted and distributed. They are based on the basic monographs Descriptive set theory (Moschovakis 1980, 2009) (posted here) and Classical Descriptive Set Theory (Kechris 1995), as well as unpublished material by Dave Marker and the Ph.D. Thesis of Vassilis Gregoriades.

Grades will be based on weekly homework.

If you are interested in the class but have questions about it, send me email.