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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