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Algebra Logika, 2018, Volume 57, Number 4, Pages 389–425 (Mi al856)  

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00247
Supported by RFBR, project No. 14-01-00376.


DOI: https://doi.org/10.17377/alglog.2018.57.401

Full text: PDF file (331 kB)
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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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\by P.~E.~Alaev
\paper Categoricity for primitive recursive and polynomial Boolean algebras
\jour Algebra Logika
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\vol 57
\issue 4
\pages 389--425
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\transl
\jour Algebra and Logic
\yr 2018
\vol 57
\issue 4
\pages 251--274
\crossref{https://doi.org/10.1007/s10469-018-9498-1}
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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. K. V. Blinov, “Primitively recursively categorical linear orderings”, Siberian Math. J., 60:1 (2019), 20–26  mathnet  crossref  crossref  isi  elib
    2. I. Sh. Kalimullin, R. Miller, “Primitivno rekursivnye polya i kategorichnost”, Algebra i logika, 58:1 (2019), 132–138  mathnet  crossref
    3. M. V. Zubkov, I. Sh. Kalimullin, A. G. Melnikov, A. N. Frolov, “Punktualnye kopii algebraicheskikh struktur”, Sib. matem. zhurn., 60:6 (2019), 1271–1285  mathnet  crossref
    4. I. Sh. Kalimullin, “O postroenii punktualno kategorichnykh polugrupp”, Algebra i logika, 59:5 (2020), 600–605  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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