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On two problems of Turing complexity for strongly minimal theories. (English. Russian original) Zbl 1152.03023
Dokl. Math. 77, No. 3, 438-440 (2008); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 420, No. 5, 589-591 (2008).
From the text: One of the directions in computable model theory is connected to the study of the complexity of theories with computable models and to algorithmic complexity of other models of such theories. Let $$T$$ be a consistent first-order theory. When can $$T$$ be realized in a computable model? On the other hand, how complicated is it to build other models of the theory $$T$$? In other words, what is the Turing complexity of these models? These problems are connected to the fundamental question of existence of computable models with given model-theoretic and algorithmic properties, i.e., with a given specification. In the present paper, we study the algorithmic complexity of countable models of strongly minimal theories that are realized on computable models, as well as the algorithmic complexity of such theories.
##### MSC:
 03C57 Computable structure theory, computable model theory 03D15 Complexity of computation (including implicit computational complexity)
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