Definition:Order Isomorphism/Isomorphic Sets

Definition
Two ordered sets $\struct {S, \preceq_1}$ and $\struct {T, \preceq_2}$ are (order) isomorphic there exists such an order isomorphism between them.

Hence $\struct {S, \preceq_1}$ is described as (order) isomorphic to (or with) $\struct {T, \preceq_2}$, and vice versa.

This may be written $\struct {S, \preceq_1} \cong \struct {T, \preceq_2}$.

Where no confusion is likely to arise, it can be abbreviated to $S \cong T$.