Given two partially ordered sets (S, <=) and (T, [=) an order isomorphism from (S, <=) to (T, [=) is an isomorphism from S to T that preserves the order, that is, it is a bijection h : S -> T such that for all u and v in S it holds that
- h(u) [= h(v) if and only if u <= v.
An order isomorphism from (S,<=) to itself is called an order automorphism