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 157, Pages 106–134 (Mi into409)  
This article is cited in 3 scientific papers (total in 3 papers)

Precomplete numberings

V. L. Selivanovab

a A.P. Ershov Institute of Informatics Systems, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Kazan (Volga Region) Federal University
Full-text PDF (399 kB) Citations (3)
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Abstract: In this survey, we discuss the theory of precomplete numberings which appear frequently in computability theory. Precomplete numberings are closely related to some variants of fixed point theorem having an important methodological value. This sometimes permits to eliminate cumbersome proofs involving the so called priority method in favour of elegant and simple applications of this theorem. In a sense, this paper covers the part of computability theory that may be developed by elementary methods.
Keywords: numbering, precomplete numbering, complete numbering, universality, reducibility, hierarchy, 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 96–124
DOI: https://doi.org/10.1007/s10958-021-05422-2
Bibliographic databases:
Document Type: Article
UDC: 510.5, 512.565.2
MSC: 03D45, 03C57
Language: Russian
Citation: V. L. Selivanov, “Precomplete numberings”, 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, 106–134; J. Math. Sci. (N. Y.), 256:1 (2021), 96–124
Citation in format AMSBIB
\Bibitem{Sel18}
\by V.~L.~Selivanov
\paper Precomplete numberings
\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 106--134
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into409}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3940085}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2021
\vol 256
\issue 1
\pages 96--124
\crossref{https://doi.org/10.1007/s10958-021-05422-2}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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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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