MATH 591. Model Theory.

Structures, theories, and definable sets; elementary equivalence and elementary embeddings; compactness and Löwenheim– Skolem theorems; types, the omitting types theorem, and saturation; categoricity and the Ryll-Nardzewski theorem; quantifier elimination and applications to algebra; ultraproducts; homogeneous structures and Fraïssé theory; infinitary logics. Optional topics: indiscernibles and Morley's theorem; stability; o-minimality; elimination of imaginaries.