Order-isomorphism

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.

If there is an order isomorphism between two partially ordered sets then these sets are called order isomorphic.

An order isomorphism from (S,<=) to itself is called an order automorphism