\begin{definition}[Definition:Order Isomorphism/Isomorphic Sets]
Two ordered sets $\struct {S, \preceq_1}$ and $\struct {T, \preceq_2}$ are '''(order) isomorphic''' if 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 $S \cong T$.
\end{definition}