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Classes of functions of the k-valued logic monotone with respect to sets of width two

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A criterion of the property of being finitely generated is obtained for precomplete classes of functions monotone with respect to sets from the family of all partially ordered sets of width two with the greatest and the least elements.

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References

  1. E. L. Post, “Introduction to a General Theory of Elementary Propositions,” Amer. J. Math. 43(3), 163 (1921).

    Article  MathSciNet  Google Scholar 

  2. E. L. Post, “The Two-Valued Iterative Systems of Mathematical Logic,” Ann. Math. Stud. Princeton Univ. Press 5 (1941).

  3. Yu. I. Yanov and A. A. Muchnik, “Existence of k-Valued Closed Classes Having no Finite Bases,” Dokl. Akad. Nauk SSSR 127(1), 44 (1959).

    MATH  MathSciNet  Google Scholar 

  4. I. G. Rosenberg, “Über die funktionale Vollständigkeit in den mehrwertigen Logiken,” Rozpr. CSAV. MPV 80, 3 (1970).

    Google Scholar 

  5. S. V. Yablonskii, G. P. Gavrilov, and A. A. Nabebin, Precomplete Classes in Multivalued Logics (Izd-vo MEI, Moscow, 1997) [in Russian].

    Google Scholar 

  6. D. Lau, “Bestimmung der Ordnung maximaler Klassen von Funktionen der k-wertigen Logik,” Z. math. Log. und Grundl. Math. 24, 79 (1978).

    Article  MATH  Google Scholar 

  7. J. Demetrovics, L. Hannák, and L. Rónyai, “Near Unanimity Functions and Partial Orderings,” in Proc. 14 ISMVL, Manitoba (1984), pp. 52–56.

  8. J. Demetrovics, L. Hannák, and L. Rónyai, “On Algebraic Properties of Monotone Clones,” Order 3, 219 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  9. K. Baker and A. Pixley, “Polynomial Interpolation and the" Chinese Remainder Theorem for Algebraic Systems,” Math. Z. 143, 165 (1975).

    Article  MATH  MathSciNet  Google Scholar 

  10. G. Tardos, “A not Finitely Generated Maximal Clone of Monotone Operations,” Order 3, 211 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  11. O. S. Dudakova, “On Some Family of Precomplete Classes of Functions of k-Valued Logic not Having a Finite Basis,” Vestn. Mosk. Univ., Matem. Mekhan. No. 2, 29 (2006) [Moscow Univ. Math. Bull. No. 2, 29 (2006)].

  12. O. S. Dudakova, “Properties of Precomplete Classes of Monotone Functions of the k-Valued Logics,” in Proc. VII Int. Conf. “Discrete Models in the Theory of Control Systems” (Pokrovskoe, March 4–6, 2006) (MAKS Press, Moscow, 2006), pp. 107–113.

    Google Scholar 

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Original Russian Text © O.S. Dudakova, 2008, published in Vestnik Moskovskogo Universiteta, Matematika, Mekhanika, 2008, Vol. 63, No. 1, pp. 31–37.

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Dudakova, O.S. Classes of functions of the k-valued logic monotone with respect to sets of width two. Moscow Univ. Math. Bull. 63, 33–38 (2008). https://doi.org/10.1007/s11970-008-1007-7

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  • DOI: https://doi.org/10.1007/s11970-008-1007-7

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