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Countability of the set of closed overclasses of some minimal classes in the partly ordered set ℒ2 3 of all closed classes of three-valued logic that can be mapped homomorphically onto two-valued logic

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Abstract

The following theorem is proved: the set of closed classes containing some minimal classes in the partly ordered set ℒ2 3 of closed classes in the three-valued logic that may be mapped homomorphically onto the two-valued logic is countable.

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References

  1. A. V. Makarov, “The Homomorphisms of Functional Systems of Multi-Valued Logics,” in: Mathematical Problems of Cybernetics, Issue 4, Ed. by S. V. Yablonskii (Nauka, Moscow, 1992), pp. 5–29.

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  2. A. V. Makarov, “The Description of all Minimal Classes in the Partly Ordered Set L32 of Closed Classes of the Three-Valued Logic that can be Homomorphically Mapped onto the Two-Valued Logic,” Vestnik Mosk. Univ., Matem. Mekhan., No. 1, 65 (2015) [Moscow Univ. Math. Bull. 70 (1), 48 (2015)].

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  3. S. V. Yablonskii, “Functional Constructions in a k-Valued Logic,” Trudy Steklov. Matem. Inst. 51, 5 (1958).

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  4. S. V. Yablonskii, G. P. Gavrilov, and V. B. Kudryavtsev, Functions of the Algebra of Logic and Post Classes (Nauka, Moscow, 1966) [in Russian].

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  5. D. N. Zhuk, “The Cardinality of the Set of all Clones Containing a Given Minimal Clone on Three Elements,” Algebra Univers. 68, 295 (2012).

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Author information

Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Leninskie Gory, Moscow State University, Moscow, 119991, Russia

    A. V. Makarov & V. V. Makarov

  2. Moscow Technological University (MIREA), 78 Vernadskii av., Moscow, 119454, Russia

    A. V. Makarov & V. V. Makarov

Authors
  1. A. V. Makarov
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  2. V. V. Makarov
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Corresponding author

Correspondence to A. V. Makarov.

Additional information

Original Russian Text © A.V. Makarov and V.V. Makarov, 2017, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2017, Vol. 72, No. 1, pp. 62–64.

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Makarov, A.V., Makarov, V.V. Countability of the set of closed overclasses of some minimal classes in the partly ordered set ℒ2 3 of all closed classes of three-valued logic that can be mapped homomorphically onto two-valued logic. Moscow Univ. Math. Bull. 72, 35–36 (2017). https://doi.org/10.3103/S0027132217010065

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  • DOI: https://doi.org/10.3103/S0027132217010065

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