Instructor: Rami Grossberg
Office: WEH 7204
Phone: x8482 (268-8482 from external lines), messages at x2545
Email: Rami@cmu.edu
URL: www.math.cmu.edu/~rami
Office Hours: By appointment or whenever else you can find me.

Purpose. This is a second course in model theory. The main topic of discussion will be classification theory for non-elemntary classes.

Course description.

I will concentrate in what is the deepest part of pure model theory. Namely non-first order theories. We will focus in abstract elementary classes. An AEC is a class K of models all of the same similarity type (or a category of sets) with a notion of an embedding which is closed under direct limits and little more. The aim is to have an analysis of such general classes. Most of the material to be discussed appears in (badly written) papers only. I will start with minimal prerequisits, but will progress quickly to some of the research frontieers of the field. I will concentrate in parts of the the theory that may eventually converge to a proof cases of Shelah's categoricity conjecture which is the prominent open problem in the field, it is a parallel to Morley's theorem for L_w1,w, most results will be about more general classes. The common to all these classes is that the compactness theorem fails badly. Hopefully some of the techniques will turn to be usefull also in the study of classes of finite models, but we will concentrate at infinite models. There will be a more serious use of set theory than needed for model theory of first-order logic.

Prerequisites: About half of a basic graduate course in set theory and parts of an elementary model theory course (about 60-70% of 21-603) or permission of the instructor.

Textbook: There is no official text.

Material for students in this course, if you use this link you agree not to forward and/or share the contents without my explicit agreement.