Mathematics 580: Topics in Set Theory: Combinatorial Set Theory.
Section 1.
Instructor: Andres Caicedo.
Time: MWF 3:40-4:30 pm.
Place: Education building, Room 330.
Office Hours: By appointment. See this page for details.
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.
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.
Textbook: There is no official textbook. The following suggested references may be useful, but are not required:
- Set theory. By T. Jech. Springer (2006), ISBN-10: 3540440852 ISBN-13: 978-3540440857
- Set theory. An introduction to independence proofs. By K. Kunen. North Holland (1983), ISBN-10: 0444868399 ISBN-13: 978-0444868398
- Set theory for the working mathematician. By K. Ciesielski. Cambridge U. Press (1997), ISBN-10: 0521594650 ISBN-13: 978-0521594653
- Set theory. By A. Hajnal and P. Hamburger. Cambridge U. Press (1999), ISBN-10: 052159667X ISBN-13: 978-0521596671
- Discovering modern set theory. By W. Just and M. Weese. Vol I. AMS (1995), ISBN-10: 0821802666 ISBN-13: 978-0821802663. Vol II. AMS (1997), ISBN-10: 0821805282 ISBN-13: 978-0821805282
- Problems and theorems in classical set theory. By P. Komjath and V. Totik. Springer (2006), ISBN-10: 038730293X ISBN-13: 978-0387302935
- Notes on set theory. By Y. Moschovakis. Springer (2005), ISBN-10: 038728723X ISBN-13: 978-0387287232
Grading: Based on homework.
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A kind of library 
YEA!
My interests in loose order of preference would be:
1) infinite trees
2) partition calculus
3) determinacy and infinite games
billy
I would like to cover some stuff on large cardinals (since questions concerning partition calculus and trees become questions concerning large cardinals so naturally) and infinite games/AD (since I really know so little about determinacy).