Elements of Model Theory

  • Wolfgang RautenbergEmail author
Part of the Universitext book series (UTX)


Model theory is a main branch of applied mathematical logic. Here the techniques developed in mathematical logic are combined with construction methods of other areas (such as algebra and analysis) to their mutual benefit. The following demonstrations can provide only a first glimpse in this respect, a deeper understanding being gained, for instance, from [CK] or [Ho]. For further-ranging topics, such as saturated models, stability theory, and the model theory of languages other than first-order, we refer to the special literature, [Bue], [Mar], [Pz], [Rot], [Sa], [She].

The theorems of Lwenheim and Skolem were first formulated in the generality given in 5.1 by Tarski. These and the compactness theorem form the basis of model theory, a now wide-ranging discipline that arose around 1950. Key concepts of model theory are elementary equivalence and elementary extension. These not only are interesting in themselves but also have multiple applications to model constructions in set theory, nonstandard analysis, algebra, geometry and elsewhere.


Winning Strategy Edge Element Elementary Extension Quotient Field Quantifier Elimination 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Fachbereich Mathematik und InformatikBerlinGermany

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