RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 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

 Algebra Logika, 2018, Volume 57, Number 2, Pages 149–174 (Mi al841)

Degrees of autostability for prime Boolean algebras

N. A. Bazhenovab, M. I. Marchukab

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia

Abstract: We look at the concept of algorithmic complexity of isomorphisms between computable copies of Boolean algebras. Degrees of autostability are found for all prime Boolean algebras. It is shown that for any ordinals $\alpha$ and $\beta$ with the condition $0\le\alpha\le\beta\le\omega$ there is a decidable model for which $\mathbf0^{(\alpha)}$ is a degree of autostability relative to strong constructivizations, while $\mathbf0^{(\beta)}$ is a degree of autostability. It is proved that for any nonzero ordinal $\beta\le\omega$, there is a decidable model for which there is no degree of autostability relative to strong constructivizations, while $\mathbf0^{(\beta)}$ is a degree of autostability.

Keywords: autostability spectrum, degree of autostability, Boolean algebra, autostability, prime model, computable model, computable categoricity, categoricity spectrum, degree of categoricity, decidable model, autostability relative to strong constructivizations.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-31-60058 ìîë_à_äê14-01-00376 Ministry of Education and Science of the Russian Federation ÍØ-6848.2016.1 Supported by RFBR, project No. 16-31-60058 mol_a_dk. Supported by RFBR (project No. 14-01-00376) and by the Grants Council (under RF President) for State Aid of Leading Scientific Schools (grant NSh-6848.2016.1).

DOI: https://doi.org/10.17377/alglog.2018.57.202

Full text: PDF file (272 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Algebra and Logic, 2018, 57:2, 98–114

Bibliographic databases:

Document Type: Article
UDC: 510.5+512.563
Revised: 25.05.2016

Citation: N. A. Bazhenov, M. I. Marchuk, “Degrees of autostability for prime Boolean algebras”, Algebra Logika, 57:2 (2018), 149–174; Algebra and Logic, 57:2 (2018), 98–114

Citation in format AMSBIB
\Bibitem{BazMar18} \by N.~A.~Bazhenov, M.~I.~Marchuk \paper Degrees of autostability for prime Boolean algebras \jour Algebra Logika \yr 2018 \vol 57 \issue 2 \pages 149--174 \mathnet{http://mi.mathnet.ru/al841} \crossref{https://doi.org/10.17377/alglog.2018.57.202} \transl \jour Algebra and Logic \yr 2018 \vol 57 \issue 2 \pages 98--114 \crossref{https://doi.org/10.1007/s10469-018-9483-8} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000440418100002} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85050685818}