On Constructive Models of Theories with Linear Rudin–Keisler Ordering

Syntactical characterisation of the class of Ehrenfeucht theories was got in [1] by Sudoplatov. It was proved that one can set any Ehrenfeucht theory by a finite pre-ordering (Rudin–Keisler pre-ordering) and a function from this pre-ordering to the set of natural numbers as parameters.
One of the main results of the paper is the next one. For all $1\leqslant n\in\omega$ there exists an Ehrenfeucht theory $T_n$ such that $RK(T_n)\cong L_n$, all quasi-prime models of $T_n$ have no computable presentations, there exists computably presentable model of $T_n$.
[1] Sudoplatov, S. V., Complete Theories with Finitely Many Countable Models // Algebra and Logic. 2004. Vol. 43. No. 1. P. 62–69.