\begin{definition}[Definition:Order Isomorphism/Definition 3]
Let $\struct {S, \preceq_1}$ and $\struct {T, \preceq_2}$ be ordered sets.
Let $\phi: S \to T$ be a bijection such that:
:$\forall x, y \in S: x \preceq_1 y \iff \map \phi x \preceq_2 \map \phi y$
Then $\phi$ is an '''order isomorphism'''.
\end{definition}