Notre Dame Journal of Formal Logic

Categoricity Spectra for Rigid Structures

Ekaterina Fokina, Andrey Frolov, and Iskander Kalimullin

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Abstract

For a computable structure M, the categoricity spectrum is the set of all Turing degrees capable of computing isomorphisms among arbitrary computable copies of M. If the spectrum has a least degree, this degree is called the degree of categoricity of M. In this paper we investigate spectra of categoricity for computable rigid structures. In particular, we give examples of rigid structures without degrees of categoricity.

Article information

Source
Notre Dame J. Formal Logic, Volume 57, Number 1 (2016), 45-57.

Dates
Received: 14 February 2013
Accepted: 26 August 2013
First available in Project Euclid: 30 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1446210671

Digital Object Identifier
doi:10.1215/00294527-3322017

Mathematical Reviews number (MathSciNet)
MR3447724

Zentralblatt MATH identifier
1359.03030

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

Keywords
computable structure rigid structure computably categorical categoricity spectrum degree of categoricity

Citation

Fokina, Ekaterina; Frolov, Andrey; Kalimullin, Iskander. Categoricity Spectra for Rigid Structures. Notre Dame J. Formal Logic 57 (2016), no. 1, 45--57. doi:10.1215/00294527-3322017. https://projecteuclid.org/euclid.ndjfl/1446210671


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References

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