Geodesic
Complexity of categorical theories with computable models
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 5 (2005) no. 2, pp. 77-85 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper 2 theorems are proved: There is an uncountably categorical but not countably categorical theory of an arbitrary given arithmetical complexity with a computable model. All countable models of this theory are computable. There is a countably categorical theory of an arbitrary given arithmetical complexity with a computable model. 
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E. Fokina. Complexity of categorical theories with computable models. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 5 (2005) no. 2, pp. 77-85. http://geodesic.mathdoc.fr/item/VNGU_2005_5_2_a4/

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