Geodesic
On Constructive Models of Theories with Linear Rudin--Keisler Ordering
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 2, pp. 30-37

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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. 
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     title = {On {Constructive} {Models} of {Theories} with {Linear} {Rudin--Keisler} {Ordering}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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A. N. Gavryushkin. On Constructive Models of Theories with Linear Rudin--Keisler Ordering. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 2, pp. 30-37. http://geodesic.mathdoc.fr/item/VNGU_2009_9_2_a2/