## Notre Dame Journal of Formal Logic

### Categoricity Spectra for Rigid Structures

#### Abstract

For a computable structure $\mathcal {M}$, the categoricity spectrum is the set of all Turing degrees capable of computing isomorphisms among arbitrary computable copies of $\mathcal {M}$. If the spectrum has a least degree, this degree is called the degree of categoricity of $\mathcal {M}$. 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
Accepted: 26 August 2013
First available in Project Euclid: 30 October 2015

https://projecteuclid.org/euclid.ndjfl/1446210671

Digital Object Identifier
doi:10.1215/00294527-3322017

Mathematical Reviews number (MathSciNet)
MR3447724

Zentralblatt MATH identifier
1359.03030

#### 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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