Math 512: Descriptive Set Theory

Fall 2002

MWF 11:00 216 Taft Hall

Instructor David Marker


It is well know that when one studies arbitrary subsets of the real numbers one runs into many pathologies (non-measurable sets) and independent problems (the Continuum Hypothesis). In Descriptive Set Theory we try to avoid these pathologies by concentrating on natural classes of well-behaved sets of reals, like Borel sets or projective sets (the smallest class of sets containing Borel sets and closed under projections from higher dimenional spaces). While this is a restricted class of sets it includes most of the sets that arise naturally in mathematical practice. Lately there have been many intersting connections with dynamical systems, through the study of orbit equivalence relations.

The first half of the course will be devoted to developing the fundamental results and techniques of descriptive set theory. In the second half we will look at more recent developments. The exact topics covered will depend on the background and interest of the class.

The topics covered may include:


Basics of topology of metric spaces, ideally students should be familiar with very basic set theory (cardinals and ordinals) and elementary measure theory, but these topics can be picked up as we go along.


I will be distributing lecture notes containing a number of exercises. Over the course of the semester you should complete and turn in 15 exercises.

Lecture Notes


Go back to Dave's Home Page