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Computable models of theories with few models. (English) Zbl 0891.03013
Summary: We investigate computable models of $$\aleph_1$$-categorical theories and Ehrenfeucht theories. For instance, we give an example of an $$\aleph_1$$-categorical but not $$\aleph_0$$-categorical theory $$T$$ such that all the countable models of $$T$$ except its prime model have computable presentations. We also show that there exists an $$\aleph_1$$-categorical but not $$\aleph_0$$-categorical theory $$T$$ such that all the countable models of $$T$$ except the saturated model, have computable presentations.

##### MSC:
 03C57 Computable structure theory, computable model theory 03C35 Categoricity and completeness of theories 03C15 Model theory of denumerable and separable structures
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##### References:
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