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



Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






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


Sibirsk. Mat. Zh., 2017, Volume 58, Number 6, Pages 1418–1427 (Mi smj2948)  

This article is cited in 3 scientific papers (total in 3 papers)

The Rogers semilattices of generalized computable enumerations

M. Kh. Faizrahmanov

Kazan (Volga Region) Federal University, Lobachevskiĭ Institute of Mathematics and Mechanics, Kazan, Russia

Abstract: We study the cardinality and structural properties of the Rogers semilattice of generalized computable enumerations with arbitrary noncomputable oracles and oracles of hyperimmune Turing degree. We show the infinity of the Rogers semilattice of generalized computable enumerations of an arbitrary nontrivial family with a noncomputable oracle. In the case of oracles of hyperimmune degree we prove that the Rogers semilattice of an arbitrary infinite family includes an ideal without minimal elements and establish that the top, if present, is a limit element under the condition that the family contains the inclusion-least set.

Keywords: computable enumeration, generalized computable enumeration, Rogers semilattice, hyperimmune set, minimal enumeration, universal enumeration.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.1515.2017/4.6
Russian Foundation for Basic Research 15-01-08252
The author was supported by the subsidy of the government task for Kazan (Volga Region) Federal University (Grant 1.1515.2017/4.6) and the Russian Foundation for Basic Research (Grant 15-01-08252).


DOI: https://doi.org/10.17377/smzh.2017.58.619

Full text: PDF file (303 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2017, 58:6, 1104–1110

Bibliographic databases:

UDC: 510.57
MSC: 35R30
Received: 16.11.2016

Citation: M. Kh. Faizrahmanov, “The Rogers semilattices of generalized computable enumerations”, Sibirsk. Mat. Zh., 58:6 (2017), 1418–1427; Siberian Math. J., 58:6 (2017), 1104–1110

Citation in format AMSBIB
\Bibitem{Fai17}
\by M.~Kh.~Faizrahmanov
\paper The Rogers semilattices of generalized computable enumerations
\jour Sibirsk. Mat. Zh.
\yr 2017
\vol 58
\issue 6
\pages 1418--1427
\mathnet{http://mi.mathnet.ru/smj2948}
\crossref{https://doi.org/10.17377/smzh.2017.58.619}
\elib{http://elibrary.ru/item.asp?id=30556287}
\transl
\jour Siberian Math. J.
\yr 2017
\vol 58
\issue 6
\pages 1104--1110
\crossref{https://doi.org/10.1134/S0037446617060192}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000425153500019}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042160448}


Linking options:
  • http://mi.mathnet.ru/eng/smj2948
  • http://mi.mathnet.ru/eng/smj/v58/i6/p1418

    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. 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
    2. M. Kh. Faizrakhmanov, “O teoreme Khutoretskogo dlya obobschenno vychislimykh semeistv”, Algebra i logika, 58:4 (2019), 528–541  mathnet  crossref
    3. M. Kh. Faizrakhmanov, “Reshetochnye svoistva polureshetok Rodzhersa vychislimykh i obobschenno vychislimykh semeistv”, Sib. elektron. matem. izv., 16 (2019), 1927–1936  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
    Number of views:
    This page:120
    Full text:26
    References:19
    First page:7

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