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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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