Syllabus
First-order structures and models, the satisfaction, an existence of models. The compactness and the completeness theorem. Embeddings and diagrams, chains of models, Lindenbaum algebras. Omitting-types theorems.
Countable categoricity. Saturated, homogenouse and universal models. Big models. Minimal and atomic models. Ultraproducts, regular and good filters. An isomorphisms theorem. Elementary classes. Indiscernibles. Model completeness.
Morley's theorem on Uncountable categoricity. The stability.
Annotation
Basic constructions of models, completeness and compactness, omitting-types theorem, Skolem functions and indiscernibles.
Automorphisms. Countable categoricity. Atomic and prime models.
Saturated, homogeneous and universal models, big models.
Ultraproducts, regular and good ultrafilters, saturativity of ultraproducts, elementary classes. Stable theories, Morley's theorem on uncountable categoricity.