Theories of linear order

Let T be a complete theory of linear order; the language of T may contain a finite or a countable set of unary predicates. We prove the following results. (i) The number of nonisomorphic countable models of T is either finite or 2^ω. (ii) If the language of T is finite then the number of nonisomorphic countable models of T is either 1 or 2^ω. (iii) If S ₁(T) is countable then so is S _n(T) for every n. (iv) In case S ₁(T) is countable we find a relation between the Cantor Bendixon rank of S ₁(T) and the Cantor Bendixon rank of S _n(T). (v) We define a class of models L, and show that S ₁(T) is finite iff the models of T belong to L. We conclude that if S ₁(T) is finite then T is finitely axiomatizable. (vi) We prove some theorems concerning the existence and the structure of saturated models.