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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2022, Number 3, Pages 11–17
(Mi vmumm4469)
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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
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.
Received: 17.11.2021
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
Linking options:
https://www.mathnet.ru/eng/vmumm4469 https://www.mathnet.ru/eng/vmumm/y2022/i3/p11
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Abstract page: | 97 | Full-text PDF : | 21 | References: | 18 | First page: | 2 |
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