# Definition:Order Type

## Definition

Let $\struct {S, \preccurlyeq_1}$ and $\struct {T, \preccurlyeq_2}$ be ordered sets.

Then $S$ and $T$ have the same (order) type if and only if they are order isomorphic.

The order type of an ordered set $\struct {S, \preccurlyeq}$ can be denoted $\map \ot {S, \preccurlyeq}$.

## Also defined as

Some sources define an order type on a totally ordered set only.

$\mathsf{Pr} \infty \mathsf{fWiki}$ prefers the more general definition.

## Also see

• Results about order types can be found here.