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.
- Wilfrid Hodges (July 20, 2009). Edward N. Zalta, ed:Model theory. The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab; Center for the Study of Language and Information. Retrieved on 2012-09-12.
- Wilfrid Hodges (April 28, 2009). Edward N. Zalta, ed:First-order model theory. The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab; Center for the Study of Language and Information. Retrieved on 2012-09-12.
- C. C. Chang, H. Jerome Keisler (2012). “§1.1 What is model theory?”, Model Theory, Reprint of North-Holland Press 1990 3rd ed. Courier Dover Publications, pp. 1 ff. ISBN 0486488217.