Geodesic
Spectra of computable models for Ehrenfeucht theories
Algebra i logika, Tome 46 (2007) no. 3, pp. 275-289.

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We construct an example of a theory with a finite (greater than one) number of isomorphism types of countable models such that its prime and saturated models have computable presentations and there exists a model which lacks in such.
Keywords: Ehrenfeucht theory, countable model, computable presentation of a model. 
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A. N. Gavryushkin. Spectra of computable models for Ehrenfeucht theories. Algebra i logika, Tome 46 (2007) no. 3, pp. 275-289. http://geodesic.mathdoc.fr/item/AL_2007_46_3_a0/

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