Notre Dame Journal of Formal Logic

Computable Models of Theories with Few Models

Bakhadyr Khoussainov, Andre Nies, and Richard A. Shore


In this paper 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.

Article information

Notre Dame J. Formal Logic, Volume 38, Number 2 (1997), 165-178.

First available in Project Euclid: 12 December 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03C15: Denumerable structures
Secondary: 03C35: Categoricity and completeness of theories 03C57: Effective and recursion-theoretic model theory [See also 03D45]


Khoussainov, Bakhadyr; Nies, Andre; Shore, Richard A. Computable Models of Theories with Few Models. Notre Dame J. Formal Logic 38 (1997), no. 2, 165--178. doi:10.1305/ndjfl/1039724885.

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