Bibliography
P. M.Cohn, Universal Algebra. New York 1965.
Forty years of Soviet Mathematics (Russian). Moscow 1957.
G. P. Gavrilov, On some completeness conditions in countably-valued logics (Russian). Dokl. Akad. Nauk SSSR128, 21–24 (1959), MR21, # 6327.
G. P. Gavrilov, On quasi-Peano functions (Russian). Dokl. Akad. Nauk SSSR156, 1011–1013 (1964); Engl. translation: Soviet Math. Dokl.156, 750–752 (1964).
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).
G. P. Gavrilov, On the functional completeness in eountably-valued logics (Russian). Problemy Kibernet.15, 5–64 (1965); Engl. translation: Systems Theory Res.15.
G.Grätzer, Universal algebra. Princeton 1968.
S. V. Iablonskii, Functional constructions in thek-valued logic (Russian). Trudy Mat. Inst. Steklov.51, 5–142 (1958).
S. V. Iablonskii, On some properties of countable closed classes fromP ℵ0 Dokl. Akad. Nauk SSSR124, 990–993 (1959); Engl. translation: Soviet Math.
Ju. I. Ianov andA. A. Mucnik, Existence ofk-valued closed classes having no finite basis (Russian). Dokl. Akad. Nauk SSSR127, 44–46 (1959).
A. I. Mal'cev, Iterative algebras and Post's varieties (Russian). Algebra i Logika5, 5–24 (1966).
E.Post, Two Valued Iterative Systems of Mathematical Logic. Ann. of Math. Studies5, Princeton 1941.
I. Rosenberg, La structure des fonctions de plusieurs variables sur un ensemble fini. C. R. Acad. Sci. Paris Ser A-B260, 3817–3819 (1965).
I. Rosenberg, Über die Verschiedenheit maximaler Klassen inP k . Rev. Roumaine Math. Pures Appl.14, 431–438 (1969).
I. Rosenberg, Über die funktionale Vollständigkeit in der mehrwertigen Logik. Rozpravy Československé Akad. Věd., Rada Mat. Příod. Vď. 80, 4, 1–93 (1970).
I. Rosenberg, The number of maximal closed classes in the set of functions over a finite domain. J. Combinatorial Theory14, 1–7 (1973).
I. G. Rosenberg, Maximal closed classes of operations on infinite sets. Math. Ann.212, 157–164 (1974).
A. Salomaa, Some Analogues of Sheffer Functions in Infinite-Valued Logics. Acta Philos. Fenn.16, 227–235 (1963).
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).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01224718