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Algebra i logika, 2016, Volume 55, Number 2, Pages 133–155
DOI: https://doi.org/10.17377/alglog.2016.55.201 (Mi al735) 		 
This article is cited in 15 scientific papers (total in 15 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
Full-text PDF (233 kB) Citations (15)
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DOI: https://doi.org/10.17377/alglog.2016.55.201
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.
Received: 07.05.2014
Revised: 03.12.2015
English version:
Algebra and Logic, 2016, Volume 55, Issue 2, Pages 87–102
DOI: https://doi.org/10.1007/s10469-016-9381-x
Bibliographic databases:
Document Type: Article
UDC: 512.563+510.5
Language: Russian
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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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и логика Algebra and Logic
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