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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 157, Pages 42–58 (Mi into406)  
This article is cited in 2 scientific papers (total in 2 papers)

Categoricity spectra of computable structures

N. A. Bazhenovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Full-text PDF (295 kB) Citations (2)
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Abstract: The categoricity spectrum of a computable structure $S$ is the set of all Turing degrees capable of computing isomorphisms among arbitrary computable presentations of $S$. The degree of categoricity of $S$ is the least degree in the categoricity spectrum of $S$. The paper gives a survey of results on categoricity spectra and degrees of categoricity for computable structures. We focus on the results about degrees of categoricity for linear orders and Boolean algebras. We build a new series of examples of degrees of categoricity for linear orders.
Keywords: computable categoricity, categoricity spectrum, degree of categoricity, computable structure, linear order, Boolean algebra, decidable categoricity, autostability, autostability relative to strong constructivizations, index set.
Funding agency Grant number
Russian Science Foundation 18-11-00028
This work was partially supported by the Russian Science Foundation (project No. 18-11-00028).
English version:
Journal of Mathematical Sciences (New York), 2021, Volume 256, Issue 1, Pages 34–50
DOI: https://doi.org/10.1007/s10958-021-05419-x
Bibliographic databases:
Document Type: Article
UDC: 510.674, 510.532, 512.56
MSC: 03C57, 03D45
Language: Russian
Citation: N. A. Bazhenov, “Categoricity spectra of computable structures”, Proceedings of the Seminar on Algebra and Mathematical Logic of the Kazan (Volga Region) Federal University, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 157, VINITI, Moscow, 2018, 42–58; J. Math. Sci. (N. Y.), 256:1 (2021), 34–50
Citation in format AMSBIB
\Bibitem{Baz18}
\by N.~A.~Bazhenov
\paper Categoricity spectra of computable structures
\inbook Proceedings of the Seminar on Algebra and Mathematical Logic of the Kazan (Volga Region) Federal University
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 157
\pages 42--58
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into406}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3940082}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2021
\vol 256
\issue 1
\pages 34--50
\crossref{https://doi.org/10.1007/s10958-021-05419-x}
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    • This publication is cited in the following 2 articles:
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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