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 157, Pages 106–134 (Mi into409)  

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

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).


Full text: PDF file (399 kB)
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Bibliographic databases:
UDC: 510.5, 512.565.2
MSC: 03D45, 03C57

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. Ser. Sovrem. Mat. Pril. Temat. Obz., 157, VINITI, Moscow, 2018, 106–134

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. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 157
\pages 106--134
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into409}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3940085}


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