Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2022, Number 3, Pages 11–17 (Mi vmumm4469)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

On the cardinality of interval Int(Pol$_k$) in partial $k$-valued logic

V. B. Alekseev

Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
Full-text PDF (335 kB) Citations (1)
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Abstract: Let Pol$_k$ be the set of all functions of $k$-valued logic representable by a polynomial modulo $k$, and let Int(Pol$_k$) be the family of all closed classes (with respect to superposition) in the partial $k$-valued logic containing Pol$_k$ and consisting only of functions extendable to some function from Pol$_k$. In this paper, we prove that if $k$ is divisible by the square of a prime number, then the family Int(Pol$_k$) contains an infinitely increasing (with respect to inclusion) chain of different closed classes. This result and the results obtained by the author earlier imply that the family Int(Pol$_k$) contains a finite number of closed classes if and only if $k$ is a prime number or a product of two different primes.
Key words: $k$-valued logic, polynomial, partial $k$-valued logic, closed class, predicate.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00200-а
The work is supported by the Russian Foundation for Basic Research, project no. 19-01-00200-a.
Received: 17.11.2021
English version:
Moscow University Mathematics Bulletin, 2022, Volume 77, Issue 3, Pages 120–126
DOI: https://doi.org/10.3103/S0027132222030032
Bibliographic databases:
Document Type: Article
UDC: 519.716
Language: Russian
Citation: V. B. Alekseev, “On the cardinality of interval Int(Pol$_k$) in partial $k$-valued logic”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2022, no. 3, 11–17; Moscow University Mathematics Bulletin, 77:3 (2022), 120–126
Citation in format AMSBIB
\Bibitem{Ale22}
\by V.~B.~Alekseev
\paper On the cardinality of interval Int(Pol$_k$) in partial $k$-valued logic
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2022
\issue 3
\pages 11--17
\mathnet{http://mi.mathnet.ru/vmumm4469}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4480996}
\zmath{https://zbmath.org/?q=an:7596804}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2022
\vol 77
\issue 3
\pages 120--126
\crossref{https://doi.org/10.3103/S0027132222030032}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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