Notre Dame Journal of Formal Logic

An Uncountably Categorical Theory Whose Only Computably Presentable Model Is Saturated

Bakhadyr Khoussainov, Denis R. Hirschfeldt, and Pavel Semukhin

Abstract

We build an א₁-categorical but not א₀-categorical theory whose only computably presentable model is the saturated one. As a tool, we introduce a notion related to limitwise monotonic functions.

Article information

Source
Notre Dame J. Formal Logic, Volume 47, Number 1 (2006), 63-71.

Dates
First available in Project Euclid: 27 March 2006

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1143468311

Digital Object Identifier
doi:10.1305/ndjfl/1143468311

Mathematical Reviews number (MathSciNet)
MR2211182

Zentralblatt MATH identifier
1107.03032

Subjects
Primary: 03045
Secondary: 03C57: Effective and recursion-theoretic model theory [See also 03D45]

Keywords
computable structure aleph 1-categoricity

Citation

Hirschfeldt, Denis R.; Khoussainov, Bakhadyr; Semukhin, Pavel. An Uncountably Categorical Theory Whose Only Computably Presentable Model Is Saturated. Notre Dame J. Formal Logic 47 (2006), no. 1, 63--71. doi:10.1305/ndjfl/1143468311. https://projecteuclid.org/euclid.ndjfl/1143468311


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References

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