Model Theory II

12 units · Graduate

Intermittent: 12 units The course concentrates in what is considered "main stream model theory" with is Shelah's classification theory (known also as Stability). Among the topics to be presented are stability, superstability, the theory of various notions of primeness, rank functions, forking calculus, the stability spectrum theorem, finite equivalence relations theorem, stable groups (up to and including the Macintyre-Cherlin-Shelah theorem on super-stable fields), and some elementary geometric model theory. If time permits also: basic facts about infinitary languages, computation of Hanf-Morley numbers; some of the Ax-Kochen-Ershov theory of model theory for fields with valuations (will apply this to solve Artin's conjecture). (Three 50 minute lectures) Prerequisites: ( 21-355 Min. grade B or 21-235 Min. grade B or 21-455 Min. grade B) and ( 21-237 Min. grade B or 21-373 Min. grade B) and 21-603 Min. grade B Course Website: http://www.math.cmu.edu/~rami/mt2.11.desc.html