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The set of maximal closed classes of operations on an infinite setA has cardinality\(2^{2^{^{\left| A \right|} } }\)

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Bibliography

  1. P. M.Cohn, Universal Algebra. New York 1965.

  2. Forty years of Soviet Mathematics (Russian). Moscow 1957.

  3. G. P. Gavrilov, On some completeness conditions in countably-valued logics (Russian). Dokl. Akad. Nauk SSSR128, 21–24 (1959), MR21, # 6327.

    Google Scholar 

  4. G. P. Gavrilov, On quasi-Peano functions (Russian). Dokl. Akad. Nauk SSSR156, 1011–1013 (1964); Engl. translation: Soviet Math. Dokl.156, 750–752 (1964).

    Google Scholar 

  5. G. P. Gavrilov, The power of sets of closed classes of finite height inP ℵ0 (Russian). Dokl. Akad. Nauk SSSR158, 506–508 (1964); Engl. translation: Soviet Math. Dokl.158, 1239–1242 (1964).

    Google Scholar 

  6. G. P. Gavrilov, On the functional completeness in eountably-valued logics (Russian). Problemy Kibernet.15, 5–64 (1965); Engl. translation: Systems Theory Res.15.

    Google Scholar 

  7. G.Grätzer, Universal algebra. Princeton 1968.

  8. S. V. Iablonskii, Functional constructions in thek-valued logic (Russian). Trudy Mat. Inst. Steklov.51, 5–142 (1958).

    Google Scholar 

  9. S. V. Iablonskii, On some properties of countable closed classes fromP ℵ0 Dokl. Akad. Nauk SSSR124, 990–993 (1959); Engl. translation: Soviet Math.

    Google Scholar 

  10. Ju. I. Ianov andA. A. Mucnik, Existence ofk-valued closed classes having no finite basis (Russian). Dokl. Akad. Nauk SSSR127, 44–46 (1959).

    Google Scholar 

  11. A. I. Mal'cev, Iterative algebras and Post's varieties (Russian). Algebra i Logika5, 5–24 (1966).

    Google Scholar 

  12. E.Post, Two Valued Iterative Systems of Mathematical Logic. Ann. of Math. Studies5, Princeton 1941.

  13. I. Rosenberg, La structure des fonctions de plusieurs variables sur un ensemble fini. C. R. Acad. Sci. Paris Ser A-B260, 3817–3819 (1965).

    Google Scholar 

  14. I. Rosenberg, Über die Verschiedenheit maximaler Klassen inP k . Rev. Roumaine Math. Pures Appl.14, 431–438 (1969).

    Google Scholar 

  15. I. Rosenberg, Über die funktionale Vollständigkeit in der mehrwertigen Logik. Rozpravy Československé Akad. Věd., Rada Mat. Příod. Vď. 80, 4, 1–93 (1970).

    Google Scholar 

  16. I. Rosenberg, The number of maximal closed classes in the set of functions over a finite domain. J. Combinatorial Theory14, 1–7 (1973).

    Google Scholar 

  17. I. G. Rosenberg, Maximal closed classes of operations on infinite sets. Math. Ann.212, 157–164 (1974).

    Google Scholar 

  18. A. Salomaa, Some Analogues of Sheffer Functions in Infinite-Valued Logics. Acta Philos. Fenn.16, 227–235 (1963).

    Google Scholar 

  19. E. Ju. Zaharova, V. B. Kudrjavcev, andS. V. Jablonskii, Precomplete classes ink-valued Logics (Russian). Dokl. Akad. Nauk SSSR186, 3 (1969); Engl. translation: Soviet Math. Dokl.10, 618–621 (1969).

    Google Scholar 

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  1. I. G. Rosenberg

    Present address: Centre de recherches mathématiques, Université de Montréal, Montréal, Canada

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    Rosenberg, I.G. The set of maximal closed classes of operations on an infinite setA has cardinality\(2^{2^{^{\left| A \right|} } }\) . Arch. Math 27, 561–568 (1976). https://doi.org/10.1007/BF01224718

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