Notre Dame Journal of Formal Logic

A New Spectrum of Recursive Models

André Nies

Abstract

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

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

Dates
First available in Project Euclid: 28 May 2002

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1022615611

Mathematical Reviews number (MathSciNet)
MR1845630

Digital Object Identifier
doi:10.1305/ndjfl/1022615611

Zentralblatt MATH identifier
1007.03036

Subjects
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]

Citation

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


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References

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