This Fall 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, with emphasis on three topics: Choice-free combinatorics, cardinal arithmetic, and partition calculus (a generalization of Ramsey theory).
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 a comment.
Pre-requisites: Permission by instructor. The recommended background is knowledge of cardinals and ordinals. A basic course on set theory (like 502: Logic and Set Theory) would be ideal but is not required.
Grading: Based on homework.
Textbook: Combinatorial set theory, by Neil H. Williams. Elsevier Science (1977). ISBN-10: 0720407222, ISBN-13: 978-0720407228. The book seems to be out of print.
We will also use:
- Combinatorial Set Theory: Partition Relations for Cardinals, by Paul Erdös, András Hajnal, Attila Máté, and Richard Rado. Elsevier Science (1984). ISBN-10: 0444861572, ISBN-13: 978-0444861573. Apparently, this is also out of print.
I will distribute notes on the material of these books, on additional topics, and some papers that we will follow, particularly:
- András Hajnal and Jean A. Larson. “Partition relations”, in Handbook of set theory, 129–213, Springer, 2010.
- Jean A. Larson. “Infinite combinatorics”, in Handbook of the history of science, vol. 6, 145-357, Elsevier, 2012.