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Algebra i logika, 2022, Volume 61, Number 3, Pages 280–307
DOI: https://doi.org/10.33048/alglog.2022.61.302
(Mi al2711)
 

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

Minimal generalized computable numberings and families of positive preorders

F. Rakymzhankyzya, N. A. Bazhenovb, A. A. Issakhova, B. S. Kalmurzayevca

a Kazakh-British Technical University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
c Al-Farabi Kazakh National University
References:
Abstract: We study $A$-computable numberings for various natural classes of sets. For an arbitrary oracle $A\geq_T \mathbf{0'}$, an example of an $A$-computable family $S$ is constructed in which each $A$-computable numbering of $S$ has a minimal cover, and at the same time, $S$ does not satisfy the sufficient conditions for the existence of minimal covers specified by S. A. Badaev and S. Yu. Podzorov in [Sib. Math. J., 43, No. 4, 616–622 (2002)]. It is proved that the family of all positive linear preorders has an $A$-computable numbering iff $A' \geq_T \mathbf{0}''$. We obtain a series of results on minimal $A$-computable numberings, in particular, Friedberg numberings and positive undecidable numberings.
Keywords: $A$-computable numbering, positive linear preorder, Rogers semilattice, Friedberg numbering, positive numbering, minimal cover.
Received: 03.11.2021
Revised: 28.10.2022
Bibliographic databases:
Document Type: Article
UDC: 510.5
Language: Russian
Citation: F. Rakymzhankyzy, N. A. Bazhenov, A. A. Issakhov, B. S. Kalmurzayev, “Minimal generalized computable numberings and families of positive preorders”, Algebra Logika, 61:3 (2022), 280–307
Citation in format AMSBIB
\Bibitem{RakBazIss22}
\by F.~Rakymzhankyzy, N.~A.~Bazhenov, A.~A.~Issakhov, B.~S.~Kalmurzayev
\paper Minimal generalized computable numberings and families of positive preorders
\jour Algebra Logika
\yr 2022
\vol 61
\issue 3
\pages 280--307
\mathnet{http://mi.mathnet.ru/al2711}
\crossref{https://doi.org/10.33048/alglog.2022.61.302}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4531968}
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  • https://www.mathnet.ru/eng/al/v61/i3/p280
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и логика Algebra and Logic
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