Included here are slides from recent talks. When viewing them I hope the reader realize that they are just one component of talks I have given and it is impossible to judge a talk based on slides only. They are posted only after several people asked me to do so.

Recent Talks

Logic and its applications in Algebra and Geometry Ann Arbor, April 11-13, 2003 \A><\a>.

TITLE: Influence of set theory on model theory
ABSTRACT: Since the early seventies some model-theoretic problems are known to be independent of ZFC, and there are several other points of contact between set theory and model theory. There is a much deeper connection: I will survey the history behind the discovery of the concepts: forking, super-stability, simplicity and excellence. In all cases set-theoretic questions were the driving force behind the discoveries. I will emphasize the role of combinatorial set theory behind some of the fundamental theorems in these areas. In recent years Hrushovski, Scanlon and Zilber to name a few, managed to use some of the most abstract results in model theory that were derived from set-theoretic considerations to obtain applications to several branches of "main-stream" mathematics. This suggests a new role for model theory as a bridge between set theory and several branches of mathematics. I plan to discuss discuss several open problems in classification theory for non-elementary classes along this line.
The slides.

Penn State Logic Seminar, January 20, 2004.

TITLE: Shelah's Categoricity Conjecture Holds for Tame AECs.
ABSTRACT: In the seventies Saharon Shelah formulated a far reaching generalization of Morley's categoricity theorem to serve as a test-problem and a guide for the development of classification theory for non-first-order-theories. Shelah's categoricity conjecture: If an L_{\omega_1,\omega} theory is categorical in a cardinal greater than the Hanf number then the theory is categorical in every cardinal above the Hanf number. Despite many papers by Shelah and others, the conjecture is still open. In the late seventies Shelah introduced the notion of abstract elementary class (a semantic generalization of L_{\omega_1,\omega} theory) and formulated a similar strong categoricity conjecture. Recently Monica VanDieren and the speaker proved that Shelah's conjecture holds for a large family of abstract elementary classes. Our proof turned to be less technical than expected, one of the surprises is that it is in ZFC, while previous related results of Shelah make heavy use of diamond-like principles. Our argument is new even when one specialize to first-order logic. In the talk I will describe all the notions in this abstract and the general framework. I intend to make my talk to be accessible also to people who did not take a course in model theory. The slides.

Last modified: January 28^th, 2004