This Spring I will be teaching Topics in set theory. The unofficial name of the course is Combinatorial Set Theory.
We will cover diverse topics in combinatorial set theory, depending on time and the interests of the audience, including partition calculus (a generalization of Ramsey theory), cardinal arithmetic, and infinite trees. Time permitting, we can also cover large cardinals, determinacy and infinite games, or cardinal invariants (the study of sizes of sets of reals), among others. I’m open to suggestions for topics, so feel free to email me or to post in the comments.
Prerequisites: Permission by instructor (that is, me).
Recommended background: Knowledge of cardinals and ordinals. A basic course on set theory (like 502: Logic and Set Theory) would be ideal but is not required.
The course may be cancelled if not enough students enroll, which would make us all rather unhappy, so don’t let this happen.
Are there any topics in descriptive set theory that would relate nicely to what you plan on covering in this course?
There are a few, indeed.
Of course, it will depend on what topics we end up emphasizing, but for example the discussion of infinite games is a natural place to mention regularity properties of sets of reals (Lebesgue measurability, Baire property, perfect set property) which is an essential ingredient of the `classical’ part of descriptive set theory, and when discussing trees one may talk about Suslin sets of reals, which easily leads to a discussion of nice dichotomy theorems for equivalence relations, which is the center of much current research in descriptive set theory.
Again, whether we end up covering all or part of this will depend on what topics we end up emphasizing as the course goes on.