PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Stephen Simpson.

Title:A vague introduction to descriptive set theory, part 1
Seminar:Logic Seminar
Speaker:John Clemens, Pennsylvania State University
Abstract:
Many examples of "pathological sets" have been produced in mathematics, such as non-Lebesgue measurable sets and well-orderings of the real numbers; however, such pathologies are rarely encountered among "natural" sets. This phenomenon can be explained by observing that sets which can be defined in an explicit manner behave more nicely than arbitrary sets. The field of descriptive set theory deals with definability of sets in Polish spaces (such as sets of real numbers). Sets which are descriptively simple (such as Borel sets) have a number of regularity properties (such as Lebesgue measurability) which may fail for arbitrary sets of reals. Conversely, many times we can prove the existence of certain functions but may be unable to provide concrete examples; sometimes, descriptive set theoretic techniques can show that no suitably definable examples exist. I will give an overview of this field, explaining what is meant by "definability" and surveying some of the common regularity properties of sets of reals.

Room Reservation Information

Room Number:MB106
Date:10 / 21 / 2008
Time:02:30pm - 03:45pm