Encyclopedia of Sciences and Religions

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

Model Theory

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


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....

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversidad de los AndesBogotáColombia