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This article is cited in 3 scientific papers (total in 3 papers)
Computable numberings of the class of Boolean algebras with distinguished endomorphisms
N. A. Bazhenovab a Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia
Abstract:
We deal with computable Boolean algebras having a fixed finite number $\lambda$ of distinguished endomorphisms (briefly, $E_\lambda$-algebras). It is shown that the index set of $E_\lambda$-algebras is $\Pi^0_\2$-complete. It is proved that the class of all computable $E_\lambda$-algebras has a $\Delta^0_3$-computable numbering but does not have a $\Delta^0_2$-computable numbering, up to computable isomorphism. Also for the class of all computable $E_\lambda$-algebras, we explore whether there exist hyperarithmetical Friedberg numberings, up to $\Delta^0_\alpha$-computable isomorphism.
Keywords:
computable Boolean algebra with distinguished endomorphisms, computable numbering, Friedberg numbering, index set, isomorphism problem.
Received: 17.07.2013
Citation:
N. A. Bazhenov, “Computable numberings of the class of Boolean algebras with distinguished endomorphisms”, Algebra Logika, 52:5 (2013), 535–552; Algebra and Logic, 52:5 (2013), 355–366
Linking options:
https://www.mathnet.ru/eng/al601 https://www.mathnet.ru/eng/al/v52/i5/p535
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Abstract page: | 278 | Full-text PDF : | 58 | References: | 68 | First page: | 24 |
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