quality:corruption, information:extraction, structural:expansion
Finite model theory

Finite model theory, which concentrates on finite structures, diverges significantly from the study of infinite structures in both the problems studied and the techniques used. In particular, many central results of classical model theory that fail when restricted to finite structures. This includes the compactness theorem, Gödel's completeness theorem, and the method of ultraproducts for first-order logic. At the interface of finite and infinite model theory are algorithmic or computable model theory and the study of 0-1 laws, where the infinite models of a generic theory of a class of structures provide information on the distribution of finite models. Prominent application areas of FMT are descriptive complexity theory, database theory and formal language theory.