This will be different than courses I offered in the last two years. It will not depend on Model theory II offered in spring 2019.

I will concentrate in classification theory for first-order theories. The theory was developed mostly by Saharon Shelah presented in his 1978 (2nd ed 1990) book and in several hundreds of papers. I will present a modern overview of Shelah's theory incorporating few recent innovations and simplifications. The development of the theory was motivated by set-theoretic questions like: "what is the asymptotic behavior of the function I(\aleph_\alpha,T) as a function of \alpha ?" and "what is the first \lambda such that an uncountable first-order stable theory T is stable in \lambda?"

Surprisingly the full answer to such combinatorial set-theoretic questions led for a development and discovery of a conceptually rich theory which seems to be related to aspects of commutative algebra and algebraic-geometry. This theory found several applications in the form of solving fundamental problems in classical fields of mathematics among them geometry and number theory.

The focus will be on the simplest and most fundamental aspects of the pure theory. Primarily around a notion called forking and various characterizations of classes of theories.

The American Mathematical Society awarded in 2013 its "Steel prize for Seminal Contribution to Research" to Shelah for his 1990 book. [the prize is given out to logicians once in 10 years, the 2003 prize was shared by Jensen & Morley]
Among the reasons given: ... made model theory into a mature field, completely transforming its aims, methods, and ability to connect to algebra and geometry."

Prerequisites: Elementary model theory (21-603) or permission of the instructor. The pace of presentation will be faster than in 21-603.

Text: Rami Grossberg, A course in model theory I: An introduction, a book in preperation.
Table of contents (as of August 2019). This is the first volume in a three volume book series to be published by Cambridge University Press. The full text is available to registered students from a protected directory here. If you use this link, you agree not to publish it and not to share the contents.

Some of the material appears in the following books:

• J. Baldwin, Fundamentals of stability theory.
• S. Buechler, Essential Stability theory.
• A. Pillay, Stability.
• Bruno Poizat, A course in Model Theory, Springer-Verlag 2000.
• Saharon Shelah, Classification Theory North-Holland 1990. This is the most important and difficult book in model theory. A free copy is available from his web site .
• Katrin Tent and Martin Ziegler, A course in model theory.