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Sibirskii Matematicheskii Zhurnal, 2019, Volume 60, Number 2, Pages 290–305
DOI: https://doi.org/10.33048/smzh.2019.60.204
(Mi smj3076)
 

This article is cited in 2 scientific papers (total in 2 papers)

Rogers semilattices for families of equivalence relations in the Ershov hierarchy

N. A. Bazhenovab, B. S. Kalmurzaevc

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
c Al-Farabi Kazakh National University, Almaty, Kazakhstan
Full-text PDF (355 kB) Citations (2)
References:
Abstract: The paper studies Rogers semilattices for families of equivalence relations in the Ershov hierarchy. For an arbitrary notation $a$ of a nonzero computable ordinal, we consider $\Sigma^{-1}_a$-computable numberings of the family of all $\Sigma^{-1}_a$ equivalence relations. We show that this family has infinitely many pairwise incomparable Friedberg numberings and infinitely many pairwise incomparable positive undecidable numberings. We prove that the family of all c.e. equivalence relations has infinitely many pairwise incomparable minimal nonpositive numberings. Moreover, we show that there are infinitely many principal ideals without minimal numberings.
Keywords: Rogers semilattice, Ershov hierarchy, equivalence relation, computable numbering, Friedberg numbering, minimal numbering, universal numbering, principal ideal.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP05131579
Russian Foundation for Basic Research 17-301-50022_мол_нр
N. A. Bazhenov was supported by the Ministry of Education and Science of the Republic of Kazakhstan (Grant AP05131579 “Positive Preorders and Computable Reducibility on Them as a Mathematical Model of Databases”). B. S. Kalmurzaev was supported by the Russian Foundation for Basic Research (Grant 17-301-50022 mol_nr).
Received: 13.06.2018
Revised: 13.06.2018
Accepted: 19.12.2018
English version:
Siberian Mathematical Journal, 2019, Volume 60, Issue 2, Pages 223–234
DOI: https://doi.org/10.1134/S0037446619020046
Bibliographic databases:
Document Type: Article
UDC: 510.55
Language: Russian
Citation: N. A. Bazhenov, B. S. Kalmurzaev, “Rogers semilattices for families of equivalence relations in the Ershov hierarchy”, Sibirsk. Mat. Zh., 60:2 (2019), 290–305; Siberian Math. J., 60:2 (2019), 223–234
Citation in format AMSBIB
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\paper Rogers semilattices for families of equivalence relations in the Ershov hierarchy
\jour Sibirsk. Mat. Zh.
\yr 2019
\vol 60
\issue 2
\pages 290--305
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\crossref{https://doi.org/10.33048/smzh.2019.60.204}
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\transl
\jour Siberian Math. J.
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\vol 60
\issue 2
\pages 223--234
\crossref{https://doi.org/10.1134/S0037446619020046}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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