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. 
@article{AL_2007_46_3_a0,
     author = {A. N. Gavryushkin},
     title = {Spectra of computable models for {Ehrenfeucht} theories},
     journal = {Algebra i logika},
     pages = {275--289},
     publisher = {mathdoc},
     volume = {46},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2007_46_3_a0/}
}
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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/