Notre Dame Journal of Formal Logic

A New Spectrum of Recursive Models

André Nies


We describe a strongly minimal theory S in an effective language such that, in the chain of countable models of S, only the second model has a computable presentation. Thus there is a spectrum of an $ \omega_{1}^{}$-categorical theory which is neither upward nor downward closed. We also give an upper bound on the complexity of spectra.

Article information

Notre Dame J. Formal Logic, Volume 40, Number 3 (1999), 307-314.

First available in Project Euclid: 28 May 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03D45: Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55]
Secondary: 03C57: Effective and recursion-theoretic model theory [See also 03D45]


Nies, André. A New Spectrum of Recursive Models. Notre Dame J. Formal Logic 40 (1999), no. 3, 307--314. doi:10.1305/ndjfl/1022615611.

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  • Baldwin, J., and A. Lachlan, “On strongly minimal sets,” The Journal of Symbolic Logic, vol. 36, (1971), pp. 79–96. Zbl 0217.30402 MR 44:3851
  • Hodges, W., Model Theory, Encyclopedia of Mathematics, Cambridge University Press, Cambridge, 1993. Zbl 0789.03031 MR 94e:03002
  • Khoussainov, B., A. Nies, and R. A. Shore, “Recursive models of theories with few models,” Notre Dame Journal of Formal Logic, vol. 38 (1997), pp. 165–78.
  • Kudeiberganov, K., “On constructive models of undecidable theories,” Sibirskiy Matematicheskiy Zhumal, vol. 21 (1980), pp. 155–58, 192.