MODEL THEORY
The metatheory of the satisfaction relation: results and techniques about the models of a logic, their construction, classification, and the definability of properties within them. Where an entry elsewhere in the collection defines a logic, an entry here proves something about the class of structures a logic can describe.
Entries include the classical theorems and tools (compactness, Löwenheim-Skolem, interpolation, ultraproducts, saturation, elementary embeddings and equivalence, quantifier elimination, the omitting types theorem), the classification programs (Morley's categoricity theorem, stability theory, o-minimality, abstract elementary classes, Fraïssé limits), the finite and generalized settings (finite model theory, descriptive complexity, continuous model theory, team, dependence, and independence-friendly logics), the abstract framing (Lindström-style abstract model theory, institutions, algebraic logics), and set-theoretic model construction (forcing, the constructible universe, Gödel's completeness theorem, Tarski's undefinability theorem). Model-theoretic accounts of natural-language meaning are cross-listed here.