Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 158, Pages 23–39 (Mi into411)  
This article is cited in 2 scientific papers (total in 2 papers)

Degree spectra of structures

I. Sh. Kalimullina, V. L. Selivanovba, A. N. Frolova

a Kazan (Volga Region) Federal University
b A.P. Ershov Institute of Informatics Systems, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (300 kB) Citations (2)
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Abstract: In this survey, we discuss computability spectra of countable structures that provide a natural measure of noncomputability of a structure. This notion is a main tool of investigating algorithmic properties of countable structures. Along with a review of known results in this field, we present proofs of some new results to illustrate the method of interpretation which is a basic method of the field. We also discuss some remaining open questions.
Keywords: structure, computable structure, spectrum of a structure, interpretation.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.451.2016/1.4
1.1515.2017/4.6
Russian Foundation for Basic Research 16-31-60077_а
Russian Science Foundation 18-11-00028
The work of I. Sh. Kalimullin was supported by the Ministry of Education and Science of the Russian Federation (project Nos. 1.1515.2017/4.6 and 1.451.2016/1.4). The work of V. L. Selivanov was supported by the Russian Science Foundation (project No. 18-11-00028). The work of A. N. Frolov was supported by the Russian Foundation for Basic Research (project No. 16-31-60077).
English version:
Journal of Mathematical Sciences (New York), 2021, Volume 256, Issue 2, Pages 143–159
DOI: https://doi.org/10.1007/s10958-021-05424-0
Bibliographic databases:
Document Type: Article
UDC: 510.5, 512.565.2
MSC: 03D45, 03C57
Language: Russian
Citation: I. Sh. Kalimullin, V. L. Selivanov, A. N. Frolov, “Degree spectra of 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., 158, VINITI, Moscow, 2018, 23–39; J. Math. Sci. (N. Y.), 256:2 (2021), 143–159
Citation in format AMSBIB
\Bibitem{KalSelFro18}
\by I.~Sh.~Kalimullin, V.~L.~Selivanov, A.~N.~Frolov
\paper Degree spectra of 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 158
\pages 23--39
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into411}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3940092}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2021
\vol 256
\issue 2
\pages 143--159
\crossref{https://doi.org/10.1007/s10958-021-05424-0}
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