Scott Rank of Automatic Partial Orderings

One of the main problems in the theory of automatic structures is the problem of characterization of automatic structures and subclasses of automatic structures. Scott ranks measure the complexity of the description of the isomorphism types of structures. M. Minnes and B. Khoussainov showed that for every ordinal $\alpha$ at most $\omega_1^{CK}+1$ there exists an automatic structure of Scott rank $\alpha$ [7;8]. In this paper we show that the same result holds for automatic partial orders.