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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Keisler G. Dzh., Chen Ch. Ch., Teoriya modelei, Mir, M., 1973

[2] Gavryushkin A. N., “Slozhnost erenfoikhtovykh modelei”, Algebra i logika, 45:5 (2006), 507–519 | MR | Zbl

[3] Gavryushkin A. N., “Spektry vychislimykh modelei erenfoikhtovykh teorii”, Algebra i logika, 46:3, 275–289 | Zbl

[4] Goncharov S. S., Ershov Yu. L., Konstruktivnye modeli, Nauchnaya kniga, Novosibirsk, 1999

[5] Khoussaainov B., Nies A., Shore R., “Computable Models of Theories with Few Models”, Notre Dame J. Form. Log., 38:2 (1997), 165–178 | DOI | MR

[6] Rodzhers Kh., Teoriya rekursivnykh funktsii i effektivnaya vychislimost, Mir, M., 1972 | MR

[7] Sudoplatov S. V., “Polnye teorii s konechnym chislom schetnykh modelei”, Algebra i logika, 43:1 (2004), 110–124 | MR | Zbl