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Algebra i logika, 2018, Volume 57, Number 3, Pages 338–361
DOI: https://doi.org/10.17377/alglog.2018.57.306 (Mi al853) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Turing degrees in refinements of the arithmetical hierarchy

V. L. Selivanovab, M. M. Yamaleevb

a Ershov Institute of Informatics Systems, pr. Akad. Lavrent'eva 6, Novosibirsk, 630090 Russia
b Kazan (Volga Region) Federal University, ul. Kremlevskaya 18, Kazan, 420008 Russia
Full-text PDF (252 kB) Citations (3)
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DOI: https://doi.org/10.17377/alglog.2018.57.306
Abstract: We investigate the problem of characterizing proper levels of the fine hierarchy (up to Turing equivalence). It is known that the fine hierarchy exhausts arithmetical sets and contains as a small fragment finite levels of Ershov hierarchies (relativized to $\varnothing^n$, $n<\omega$), which are known to be proper. Our main result is finding a least new (i.e., distinct from the levels of the relativized Ershov hierarchies) proper level. We also show that not all new levels are proper.
Keywords: Ershov hierarchy, fine hierarchy, arithmetical hierarchy, Turing degrees.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.1515.2017/4.6
Russian Science Foundation 18-11-00028
The work was carried out at the expense of the subsidy allocated to Kazan (Volga Region) Federal University for the fulfillment of the state task in the sphere of scientific activity, project No. 1.1515.2017/4.6.
Supported by Russian Science Foundation, project No. 18-11-00028.
Received: 12.12.2016
Revised: 20.10.2017
English version:
Algebra and Logic, 2018, Volume 57, Issue 3, Pages 222–236
DOI: https://doi.org/10.1007/s10469-018-9495-4
Bibliographic databases:
Document Type: Article
UDC: 510.51+510.54+510.531+510.532
Language: Russian
Citation: V. L. Selivanov, M. M. Yamaleev, “Turing degrees in refinements of the arithmetical hierarchy”, Algebra Logika, 57:3 (2018), 338–361; Algebra and Logic, 57:3 (2018), 222–236
Citation in format AMSBIB
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\paper Turing degrees in refinements of the arithmetical hierarchy
\jour Algebra Logika
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\issue 3
\pages 338--361
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\jour Algebra and Logic
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\vol 57
\issue 3
\pages 222--236
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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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    		Алгебра и логика Algebra and Logic
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