Lecturer: Rami Grossberg
Starting Date: August 25 MWF 3:30PM DH2105
This will be different than courses I offered in the past. It will not depend on Model theory II. This time I will concentrate in what is probably the deepest part of pure model theory. Namely non first-order theories. In a typical case we will deal with a class K of models all of the same similarity type (or a category of sets) 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 emphasize aspects of the theory that may eventually converge to a proof to a parallel to Morley's theorem for Lw1,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 uncountable 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 elementary model theory (half of 21-603) or permission of the instructor.
Textbook: There is no official text.