21-703 Model Theory II

12 units, Carnegie Mellon University

The course concentrates in what is considered main stream model theory with is Shelahs 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 MacintyreCherlinShelah theorem on superstable fields, and some elementary geometric model theory. If time permits also basic facts about infinitary languages, computation of HanfMorley numbers some of the AxKochenErshov theory of model theory for fields with valuations will apply this to solve Artins conjecture. Three 50 minute lectures

Prerequisites: (21-355 (min B) or 21-235 (min B) or 21-455 (min B)) and (21-237 (min B) or 21-373 (min B)) and 21-603 (min B)

Offered: Spring 2027

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