Itogi Nauki i Tekhniki. Seriya "Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory"
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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2018, Volume 158, Pages 23–39 (Mi into411)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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).


Full text: PDF file (300 kB)
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Bibliographic databases:
UDC: 510.5, 512.565.2
MSC: 03D45, 03C57

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. Ser. Sovrem. Mat. Pril. Temat. Obz., 158, VINITI, Moscow, 2018, 23–39

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. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 158
\pages 23--39
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into411}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3940092}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. V. Zubkov, A. N. Frolov, “Spektralnaya universalnost lineinykh poryadkov s odnim binarnym otnosheniem”, Sib. matem. zhurn., 61:3 (2020), 587–593  mathnet  crossref
  • Itogi Nauki i Tekhniki. Seriya "Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory" Itogi Nauki i Tekhniki. Seriya "Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory"
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