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Sibirsk. Mat. Zh., 2019, Volume 60, Number 3, Pages 599–609 (Mi smj3097)  

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

Partial decidable presentations in hyperarithmetic

I. Sh. Kalimullina, V. G. Puzarenkobc, M. Kh. Faizrahmanova

a Kazan (Volga Region) Federal University, Kazan, Russia
b Sobolev Institute of Mathematics, Novosibirsk, Russia
c Novosibirsk State University, Novosibirsk, Russia

Abstract: We study the problem of the existence of decidable and positive $\Pi_1^1$- and $\Sigma_1^1$-numberings of the families of $\Pi_1^1$- and $\Sigma_1^1$-cones with respect to inclusion. Some laws are found that reflect the presence of decidable computable $\Pi_1^1$- and $\Sigma_1^1$-numberings of these families in dependence on the analytical complexity of the set defining a cone.

Keywords: numbering, decidable numbering, positive numbering, computable numbering, computable set, computably enumerable set, $e$-reducibility, hyperarithmetic set, constructible admissible set.

Funding Agency Grant Number
Russian Science Foundation 18-11-00028
Ministry of Science and Higher Education of the Russian Federation 1.451.2016/1.4
Russian Foundation for Basic Research 18-01-00624_а
Siberian Branch of Russian Academy of Sciences 0314–2019–0003
Ministry of Education and Science of the Russian Federation 1.13556.2019/13.1
I. Sh. Kalimullin was supported by the Russian Science Foundation (Grant 18-11-00028) and by the subsidy of the Government Task for Kazan (Volga Region) Federal University (Grant 1.451.2016/1.4). V. G. Puzarenko was supported by the Russian Foundation for Basic Research (Grant 18-01-00624) and by the Program of Basic Scientific Research of the Siberian Branch of the Russian Academy of Sciences (Grant No. Project 0314-2019-0003). M. Kh. Faizrahmanov was supported by the subsidy of the Government Task for Kazan (Volga Region) Federal University (Grant 1.13556.2019/13.1).


DOI: https://doi.org/10.33048/smzh.2019.60.309

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English version:
Siberian Mathematical Journal, 2019, 60:3, 464–471

Bibliographic databases:

UDC: 510.5
Received: 08.06.2018
Revised: 25.10.2018
Accepted:19.11.2018

Citation: I. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faizrahmanov, “Partial decidable presentations in hyperarithmetic”, Sibirsk. Mat. Zh., 60:3 (2019), 599–609; Siberian Math. J., 60:3 (2019), 464–471

Citation in format AMSBIB
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\paper Partial decidable presentations in hyperarithmetic
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\pages 464--471
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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. I. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faizrakhmanov, “O pozitivnykh i odnoznachnykh vychislimykh numeratsiyakh v giperarifmetike”, Algebra i logika, 59:1 (2020), 66–83  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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