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 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.

prefers the more general definition.