Two totally ordered sets (A, <=) and (B, <=) are order isomorphic iff there is a bijection f from A to B such that for all a_1, a_2 element A, a_1<=a_2 i f f f(a_1)<=f(a_2) (Ciesielski 1997, p. 38). In other words, A and B are equipollent ("the same size") and there is an order preserving mapping between the two. Dauben and Suppes call this property "similar." The definition works equally well on partially ordered sets.
