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Model Theory

Model theory is a general theory of interpretations of Axiomatic Set Theory. It is the branch of Logic studying mathematical structures by considering first-order sentences which are true of those structures and the sets which are definable in those structures by first-order Formulas (Marker 1996).

Mathematical structures obeying axioms in a system are called ``models'' of the system. The usual axioms of Analysis are second order and are known to have the Real Numbers as their unique model. Weakening the axioms to include only the first-order ones leads to a new type of model in what is called Nonstandard Analysis.

See also Khovanski's Theorem, Nonstandard Analysis, Wilkie's Theorem


Doets, K. Basic Model Theory. New York: Cambridge University Press, 1996.

Marker, D. ``Model Theory and Exponentiation.'' Not. Amer. Math. Soc. 43, 753-759, 1996.

Stewart, I. ``Non-Standard Analysis.'' In From Here to Infinity: A Guide to Today's Mathematics. Oxford, England: Oxford University Press, pp. 80-81, 1996.

© 1996-9 Eric W. Weisstein