"In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold)."
Study of models of theories and their properties.
"The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself."
"Model theory goes back to Alfred Tarski, who first used the term 'Theory of Models' in publication in 1954."
"Since the 1970s, the subject has been shaped decisively by Saharon Shelah's stability theory."
"Compared to other areas of mathematical logic such as proof theory, model theory is often less concerned with formal rigor and closer in spirit to classical mathematics."
"This has prompted the comment that 'if proof theory is about the sacred, then model theory is about the profane'."
"The applications of model theory to algebraic and Diophantine geometry reflect this proximity to classical mathematics."
"Integration of algebraic and model-theoretic results and techniques."
"Proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature."
"The most prominent scholarly organization in the field of model theory is the Association for Symbolic Logic."
"Model theory is the study of the relationship between formal theories and their models."
"The main focus of model theory is the relationship between formal theories and the structures in which the statements of the theory hold."
"Model theory investigates the relationship of different models to each other."
"Model theory investigates the interaction of models with the formal language itself."
"Saharon Shelah's stability theory has decisively shaped the subject since the 1970s."
"Model theory is often referred to as 'about the profane' compared to proof theory, which is 'about the sacred'."
"The applications of model theory to algebraic and Diophantine geometry reflect a closer integration of algebraic and model-theoretic results and techniques."
"Model theory is often less concerned with formal rigor and closer in spirit to classical mathematics."
"Proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature."
"The most prominent scholarly organization in the field of model theory is the Association for Symbolic Logic."