RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
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 Logika, 2016, Volume 55, Number 2, Pages 133–155 (Mi al735)  

Degrees of autostability relative to strong constructivizations for Boolean algebras

N. A. Bazhenovabc

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia
c Kazan (Volga Region) Federal University, ul. Kremlevskaya 18, Kazan, 420008 Russia

Abstract: It is proved that for every computable ordinal $\alpha$, the Turing degree $\mathbf0^{(\alpha)}$ is a degree of autostability of some computable Boolean algebra and is also a degree of autostability relative to strong constructivizations for some decidable Boolean algebra. It is shown that a Harrison Boolean algebra has no degree of autostability relative to strong constructivizations. It is stated that the index set of decidable Boolean algebras having degree of autostability relative to strong constuctivizations is $\Pi^1_1$–complete.

Keywords: autostability, Boolean algebra, autostability relative to strong constructivizations, degree of autostability, degree of categoricity, index set.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-6848.2016.1
Russian Foundation for Basic Research 14-01-00376
Supported by the Grants Council (under RF President) for State Aid of Leading Scientific Schools (grant NSh-6848.2016.1), by RFBR (project No. 14-01-00376), and by the Russian Government Program of Competitive Growth of Kazan (Volga Region) Federal University.


DOI: https://doi.org/10.17377/alglog.2016.55.201

Full text: PDF file (233 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Algebra and Logic, 2016, 55:2, 87–102

Bibliographic databases:

Document Type: Article
UDC: 512.563+510.5
Received: 07.05.2014
Revised: 03.12.2015

Citation: N. A. Bazhenov, “Degrees of autostability relative to strong constructivizations for Boolean algebras”, Algebra Logika, 55:2 (2016), 133–155; Algebra and Logic, 55:2 (2016), 87–102

Citation in format AMSBIB
\Bibitem{Baz16}
\by N.~A.~Bazhenov
\paper Degrees of autostability relative to strong constructivizations for Boolean algebras
\jour Algebra Logika
\yr 2016
\vol 55
\issue 2
\pages 133--155
\mathnet{http://mi.mathnet.ru/al735}
\crossref{https://doi.org/10.17377/alglog.2016.55.201}
\transl
\jour Algebra and Logic
\yr 2016
\vol 55
\issue 2
\pages 87--102
\crossref{https://doi.org/10.1007/s10469-016-9381-x}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000382002800001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84981194391}


Linking options:
  • http://mi.mathnet.ru/eng/al735
  • http://mi.mathnet.ru/eng/al/v55/i2/p133

    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
  • Алгебра и логика Algebra and Logic
    Number of views:
    This page:32
    References:5

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2017