# nLab elementary class of structures

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.

category: model theory

Revised on April 16, 2013 16:17:46 by Zoran Škoda (161.53.130.104)