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



Sib. Èlektron. Mat. Izv.:
Year:
Volume:
Issue:
Page:
Find






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


Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 1927–1936 (Mi semr1179)  

Mathematical logic, algebra and number theory

Lattice properties of Rogers semilattices of compuatble and generalized computable familie

M. Kh. Faizrahmanov

Kazan (Volga Region) Federal University, 18, Kremlyovskaya str., Kazan, 420008, Russia

Abstract: We consider the distributivity property and the property of being a lattice of Rogers semilattices of generalized computable families. We prove that the Rogers semilattice of any nontrivial $A$-computable family is not a lattice for every non-computable set $A$. It is also proved that if a set $A$ is non-computable then the Rogers semilattice of any infinite $A$-computable family is not weakly distribuive. Furtermore, we find two infinite computable families with nontrivial distributive and properly weakly distributive nontrivial Rogers semilattices.

Keywords: computable enumeration, generalized computable enumeration, $A$-computable enumeration, Rogers semilattice.

Funding Agency Grant Number
Russian Science Foundation 18-11-00028


DOI: https://doi.org/10.33048/semi.2019.16.138

Full text: PDF file (170 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 510.5
MSC: 03D45
Received August 12, 2019, published December 18, 2019

Citation: M. Kh. Faizrahmanov, “Lattice properties of Rogers semilattices of compuatble and generalized computable familie”, Sib. Èlektron. Mat. Izv., 16 (2019), 1927–1936

Citation in format AMSBIB
\Bibitem{Fai19}
\by M.~Kh.~Faizrahmanov
\paper Lattice properties of Rogers semilattices of compuatble and generalized computable familie
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 1927--1936
\mathnet{http://mi.mathnet.ru/semr1179}
\crossref{https://doi.org/10.33048/semi.2019.16.138}


Linking options:
  • http://mi.mathnet.ru/eng/semr1179
  • http://mi.mathnet.ru/eng/semr/v16/p1927

    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
  • Number of views:
    This page:61
    Full text:13
    References:2

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