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Algebra i logika, 2021, Volume 60, Number 2, Pages 195–209
DOI: https://doi.org/10.33048/alglog.2021.60.206
(Mi al2658)
 

Some properties of the upper semilattice of computable families of computably enumerable sets

M. Kh. Faizrakhmanov

Kazan (Volga Region) Federal University
References:
Abstract: We look at specific features of the algebraic structure of an upper semilattice of computable families of computably enumerable sets in $\Omega$. It is proved that ideals of minuend and finite families of $\Omega$ coincide. We deal with the question whether there exist atoms and coatoms in the factor semilattice of $\Omega$ with respect to an ideal of finite families. Also we point out a sufficient condition for computable families to be complemented.
Keywords: computably enumerable set, computable family, computable numbering, semilattice of computable families.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2021-1393
Russian Science Foundation 18-11-00028
The work was carried out as part of the developmental program for the Science Education Mathematical Center (SEMC) in Volga Federal District, Agreement No. 075-02-2021-1393, and supported by Russian Science Foundation, project No. 18-01-00028.
Received: 11.10.2020
Revised: 24.08.2021
English version:
Algebra and Logic, 2021, Volume 60, Issue 2, Pages 128–138
DOI: https://doi.org/10.1007/s10469-021-09635-x
Bibliographic databases:
Document Type: Article
UDC: 510.5
Language: Russian
Citation: M. Kh. Faizrakhmanov, “Some properties of the upper semilattice of computable families of computably enumerable sets”, Algebra Logika, 60:2 (2021), 195–209; Algebra and Logic, 60:2 (2021), 128–138
Citation in format AMSBIB
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\paper Some properties of the upper semilattice of computable families of computably enumerable sets
\jour Algebra Logika
\yr 2021
\vol 60
\issue 2
\pages 195--209
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\crossref{https://doi.org/10.33048/alglog.2021.60.206}
\transl
\jour Algebra and Logic
\yr 2021
\vol 60
\issue 2
\pages 128--138
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