# nLab elementary class of structures

model theory

## Dimension, ranks, forking

• forking and dividing?

• Morley rank?

• Shelah 2-rank?

• Lascar U-rank?

• Vapnik–Chervonenkis dimension?

# 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 February 23, 2017 02:33:24 by Urs Schreiber (78.45.5.227)