# Model theory

## Contents

**Model theory** is the study of the interpretation of any language, formal or natural, by means of set-theoretic structures.^{[1]} Its primary branch is a field of mathematics, sometimes referred to as **first-order model theory**.^{[2]}

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.^{[3]}

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.^{[3]}

## References

- ↑
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. - ↑
^{3.0}^{3.1}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.