MATH 7870: Set Theory (spring 2009)

Instructor: Justin Moore

This course will provide an introduction to set theory and infinite combinatorics. The course will be divided into three sections:

1. Combinatorial set theory: ordinals and transfinite induction, stationary sets and the club filter, ultrafilters and ultrapowers.
2. Descriptive set theory: the boundedness and separation theorems for analytic sets, Hurewicz phenomena, uniformization and selection theorems.
3. Methods associated with independence: forcing, large cardinals, constructibility.

No text will be required for this course. Much of the material is selected from the following books (which will be placed on reserve): Kanamori's The Higher Infinite, Kechris's Classical Descriptive Set Theory, Kunen's Set Theory.

There are no strict prerequisites for this course, although students will benefit from some prior exposure to mathematical logic.