# Contents

## Definition

A class $K$ of structures of a given signature is an elementary class if there is a first-order theory $T$ such that $K$ consists precisely of all models of $T$.

There is a vast generalizations for higher-order theories (and more) abstract elementary class, metric abstract elementary class.

## References

category: model theory

Revised on March 26, 2014 03:57:14 by Urs Schreiber (185.37.147.12)