For more information about this meeting, contact Stephen Simpson.
|Title:||A vague introduction to descriptive set theory, part 1|
|Speaker:||John Clemens, Pennsylvania State University|
|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
|Date:||10 / 21 / 2008|
|Time:||02:30pm - 03:45pm|