Model theory

The course starts with detailed proofs of compactness and omitting types for first-order logic. Students is then introduced to a number of central methods, constructions and results with a focus on model completeness, automorphism groups and omega categoricity, ultraproducts, o-minimality, interpretability and back-and-forth equivalence. Quantifier elimination and zero-one laws serve as an introduction to applications of model theory to computer science. The course also deals with Morley's theorem and the basics of stability theory.