Definition 4.2 Let u and be order types represented by chains M and N. We say that v if there exists an order isomorphism f of M into N. We write u The relation between order types is reflexive and transitive but it is not antisymmetric - for example, let and be order types of the intervals (0, 1) and [0, 1]: then Therefore is not even a partial ordering among order types. and v but v.