Model theory

Model theory is the study of the interpretation of any language, formal or natural, by means of set-theoretic structures. Its primary branch is a field of mathematics, sometimes referred to as first-order model theory.

Typically, model theory begins by specifying a list of symbols and rules for forming sentences from these symbols. An assembly of such sentences and their evaluation as true or false constitutes a model. Thus, a sentence p might be assigned the value true in model M, and M is said to be a model of p. It is said that M is a model of a set of sentences if and only if M is a model of each sentence in the set.

Classical model theory proves various propositions about models, an example being "there is no set of sentences whose models constitute all possible finite models". A great deal of model theory consists of finding ways to construct models that enable proofs of various theorems.