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This article is cited in 4 scientific papers (total in 4 papers)
Categoricity for primitive recursive and polynomial Boolean algebras
P. E. Alaevab
a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia
Abstract:
We define a class $\mathbb K_\Sigma$ of primitive recursive structures whose existential diagram is decidable with primitive recursive witnesses. It is proved that a Boolean algebra has a presentation in $\mathbb K_\Sigma$ iff it has a computable presentation with computable set of atoms. Moreover, such a Boolean algebra is primitive recursively categorical with respect to $\mathbb K_\Sigma$ iff it has finitely many atoms. The obtained results can also be carried over to Boolean algebras computable in polynomial time.
Keywords:
Boolean algebra, Boolean algebra computable in polynomial time, computable presentation, primitive recursively categorical Boolean algebra.
DOI:
https://doi.org/10.17377/alglog.2018.57.401
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English version:
Algebra and Logic, 2018, 57:4, 251–274
Bibliographic databases:
 
UDC:
510.52+512.563+510.67
Received: 10.05.2017
Revised: 03.09.2018
Citation:
P. E. Alaev, “Categoricity for primitive recursive and polynomial Boolean algebras”, Algebra Logika, 57:4 (2018), 389–425; Algebra and Logic, 57:4 (2018), 251–274
Citation in format AMSBIB
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\jour Algebra Logika
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\issue 4
\pages 389--425
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\jour Algebra and Logic
\yr 2018
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\issue 4
\pages 251--274
\crossref{https://doi.org/10.1007/s10469-018-9498-1}
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Linking options:
http://mi.mathnet.ru/eng/al856 http://mi.mathnet.ru/eng/al/v57/i4/p389
Citing articles on Google Scholar:
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This publication is cited in the following articles:
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K. V. Blinov, “Primitively recursively categorical linear orderings”, Siberian Math. J., 60:1 (2019), 20–26
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I. Sh. Kalimullin, R. Miller, “Primitivno rekursivnye polya i kategorichnost”, Algebra i logika, 58:1 (2019), 132–138
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M. V. Zubkov, I. Sh. Kalimullin, A. G. Melnikov, A. N. Frolov, “Punktualnye kopii algebraicheskikh struktur”, Sib. matem. zhurn., 60:6 (2019), 1271–1285
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I. Sh. Kalimullin, “O postroenii punktualno kategorichnykh polugrupp”, Algebra i logika, 59:5 (2020), 600–605
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