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.

**References**

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

1999-05-26