Algebra i logika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Algebra Logika:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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 2 scientific papers (total in 2 papers)

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
Full-text PDF (1155 kB) Citations (2)
References:
PDF
HTML
DOI: https://doi.org/10.33048/alglog.2022.61.302
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.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP08856493
Ministry of Science and Higher Education of the Russian Federation 0314-2019-0002
F. Rakymzhankyzy, N. A. Bazhenov, A. A. Issakhov, B. S. Kalmurzayev are supported by SC MES RK, project No. AP08856493. N. A. Bazhenov was carried out as part of the state assignment to Sobolev Institute of Mathematics SB RAS, project No. 314-2019-0002.
Received: 03.11.2021
Revised: 28.10.2022
English version:
Algebra and Logic, 2022, Volume 61, Issue 3, Pages 188–206
DOI: https://doi.org/10.1007/s10469-022-09688-6
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; Algebra and Logic, 61:3 (2022), 188–206
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}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4531968}
\transl
\jour Algebra and Logic
\yr 2022
\vol 61
\issue 3
\pages 188--206
\crossref{https://doi.org/10.1007/s10469-022-09688-6}
Linking options:
  • https://www.mathnet.ru/eng/al2711
  • https://www.mathnet.ru/eng/al/v61/i3/p280
    • 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
    		Алгебра и логика Algebra and Logic
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025