Model theory

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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

  1. 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.
  2. 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. 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.