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Algebra Logika, 2016, Volume 55, Number 2, Pages 133–155 (Mi al735)  

This article is cited in 6 scientific papers (total in 6 papers)

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

Bibliographic databases:

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
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\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
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\crossref{https://doi.org/10.17377/alglog.2016.55.201}
\transl
\jour Algebra and Logic
\yr 2016
\vol 55
\issue 2
\pages 87--102
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    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. N. Bazhenov, “Autostability spectra for decidable structures”, Math. Struct. Comput. Sci., 28:3, SI (2018), 392–411  crossref  mathscinet  isi  scopus
    2. N. A. Bazhenov, M. I. Marchuk, “Degrees of autostability for prime Boolean algebras”, Algebra and Logic, 57:2 (2018), 98–114  mathnet  crossref  crossref  isi
    3. N. A. Bazhenov, M. I. Marchuk, “Degrees of autostability relative to strong constructivizations of graphs”, Siberian Math. J., 59:4 (2018), 565–577  mathnet  crossref  crossref  isi  elib
    4. N. A. Bazhenov, “Spektry kategorichnosti vychislimykh struktur”, Trudy seminara kafedry algebry i matematicheskoi logiki Kazanskogo (Privolzhskogo) federalnogo universiteta, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 157, VINITI RAN, M., 2018, 42–58  mathnet  mathscinet
    5. M. I. Marchuk, “Razreshimaya kategorichnost pochti prostykh modelei signatury grafov”, Matem. tr., 24:1 (2021), 117–141  mathnet  crossref
    6. S. S. Goncharov, M. I. Marchuk, “O stepeni razreshimoi kategorichnosti modeli s beskonechnymi resheniyami dlya polnykh formul”, Algebra i logika, 60:3 (2021), 303–312  mathnet
  • Алгебра и логика Algebra and Logic
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