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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
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.
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
Linking options:
https://www.mathnet.ru/eng/al735 https://www.mathnet.ru/eng/al/v55/i2/p133
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