Encyclopedia of Sciences and Religions

2013 Edition
| Editors: Anne L. C. Runehov, Lluis Oviedo

Model Theory

Reference work entry
DOI: https://doi.org/10.1007/978-1-4020-8265-8_1275

Description

In a broad sense,  model theory is the branch of mathematical logic that studies the connection between formal languages and their interpretations, the latter construed as relational structures. In this setting, the structures obeying the axioms of a formal theory are called the “models” of the theory. More restrictedly, it means the study of models of  first-order theories (Chang and Keisler 1973; Hodges 1993; Marcja and Toffalori 2003). Besides its foundational character, the model theory of first-order logic has become in the latter years one of the finest tools to solve classical mathematical problems, it has, moreover, strong relevance for other disciplines ranging from computer science to philosophy. Since the emergence of Syllogistics in Greece, the general trend of the development of logic was a gradual elimination of any ontological commitment, movement that culminated with the full formalization of mathematical theories at the beginning of the twentieth century....

This is a preview of subscription content, log in to check access

References

  1. Barwise, J., & Feferman, S. (1986). Model-theoretic logics. Perspectives in mathematical logic. New York: Springer.Google Scholar
  2. Chang, C. C., & Keisler, H. J. (1973). Model theory, studies in logic and the foundations of mathematics. Amsterdam: North-Holland (Elsevier, 1990, 3rd ed.).Google Scholar
  3. Cohen, P. (1966). Set theory and the continuum hypothesis. New York: Benjamin.Google Scholar
  4. Gödel, K. (1930). Die Völlstandigkeit der Axiome des logischen Funktionenkalküls. Monatshefte für Mathematik und Physik, 37, 349–360.Google Scholar
  5. Goldblat, R. I. (1979). Topoi, the categorical analysis of logic. Amsterdam: North Holland.Google Scholar
  6. Hodges, W. (1993). Model theory. Cambridge: Cambridge University Press.Google Scholar
  7. Marcja, A., & Toffalori, C. (2003). A guide to classical and modern model theory. Dordrecht: Kluwer.Google Scholar
  8. Robinson, A. (1963). Introduction to model theory and to the Metamathematics of Algebra. Amsterdam: North Holland.Google Scholar
  9. Shelah, S. (1990). Classification theory. Amsterdam: North-Holland.Google Scholar
  10. Tarski, A. (1954). Contributions to the theory of models I. Indagationes Mathematicae, 16, 572–581.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversidad de los AndesBogotáColombia