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

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 Logika, 2015, Volume 54, Number 3, Pages 305–314 (Mi al695)  

This article is cited in 4 scientific papers (total in 4 papers)

Ideals without minimal elements in Rogers semilattices

A. A. Issakhov

Al-Farabi Kazakh National University, Al-Farabi Ave. 71, Alma-Ata, 050038, Kazakhstan

Abstract: We prove a criterion for the existence of a minimal numbering, which is reducible to a given numbering of an arbitrary set. The criterion is used to show that, for any infinite $A$-computable family $F$ of total functions, where $\varnothing'\le_TA$, the Rogers semilattice $\mathcal R_A(F)$ of $A$-computable numberings for $F$ contains an ideal without minimal elements.

Keywords: minimal numbering, $A$-computable numbering, Rogers semilattice, ideal.

DOI: https://doi.org/10.17377/alglog.2015.54.301

Full text: PDF file (136 kB)
References: PDF file   HTML file

English version:
Algebra and Logic, 2015, 54:3, 197–203

Bibliographic databases:

UDC: 510.54
Received: 06.11.2014

Citation: A. A. Issakhov, “Ideals without minimal elements in Rogers semilattices”, Algebra Logika, 54:3 (2015), 305–314; Algebra and Logic, 54:3 (2015), 197–203

Citation in format AMSBIB
\Bibitem{Iss15}
\by A.~A.~Issakhov
\paper Ideals without minimal elements in Rogers semilattices
\jour Algebra Logika
\yr 2015
\vol 54
\issue 3
\pages 305--314
\mathnet{http://mi.mathnet.ru/al695}
\crossref{https://doi.org/10.17377/alglog.2015.54.301}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3467189}
\transl
\jour Algebra and Logic
\yr 2015
\vol 54
\issue 3
\pages 197--203
\crossref{https://doi.org/10.1007/s10469-015-9340-y}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000363940600001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84944936963}


Linking options:
  • http://mi.mathnet.ru/eng/al695
  • http://mi.mathnet.ru/eng/al/v54/i3/p305

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Issakhov, “Hyperimmunity and A-computable universal numberings”, International Conference on Analysis and Applied Mathematics (ICAAM 2016), AIP Conf. Proc., 1759, ed. A. Ashyralyev, A. Lukashov, Amer. Inst. Phys., 2016, 020106  crossref  isi  scopus
    2. M. Kh. Faizrahmanov, “The Rogers semilattices of generalized computable enumerations”, Siberian Math. J., 58:6 (2017), 1104–1110  mathnet  crossref  crossref  isi  elib
    3. I. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faizrahmanov, “Positive presentations of families relative to $e$-oracles”, Siberian Math. J., 59:4 (2018), 648–656  mathnet  crossref  crossref  isi  elib
    4. S. A. Badaev, A. A. Issakhov, “Some absolute properties of $A$-computable numberings”, Algebra and Logic, 57:4 (2018), 275–288  mathnet  crossref  crossref  isi
  • Алгебра и логика Algebra and Logic
    Number of views:
    This page:186
    Full text:38
    References:31
    First page:9

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020