Definition:Isomorphism Class (Ordered Structures)

Definition
Let $\struct {S, \preccurlyeq}$ be an ordered structure.

Let $\map \II {S, \preccurlyeq}$ be the class of all ordered structures which are order isomorphic to $S$.

Then $\map \II {S, \preccurlyeq}$ is known as the isomorphism class of $\struct {S, \preccurlyeq}$.