References
J. Bagyinszki andJ. Demetrovics, The structure of the maximal linear classes in primevalued logics. C.R. Math. Rep. Acad. Sci. Canada2, 209–213 (1980).
V. G. Bodnarčuk, L. A. Kalužnin, V. N. Kotov andB. A. Romov, Galois theory for Post algebras, I–II (Russian). Kibernetika5, 1–10 (1969), and5, 1–9 (1969); English translation: Cybernetics5, 243–252 and 531–539 (1969).
G. A. Burle, The classes ofk-valued logics containing all one variable functions (Russian). Diskret. Analiz10, 3–7 (1967).
B. Csákány, Homogeneous algebras are functionally complete. Algebra Universalis11, 149–158 (1980).
J. Demetrovics andL. Hannák, On the cardinality of self-dual closed classes ink-valued logics. Közl. — MTA Számítástech. Automat. Kutató Int. Budapest22, 7–18 (1979).
J. Demetrovics, L. Hannák andL. Rónyai, Almost all prime-element algebras with transitive automorphism groups are functionally complete, in: Finite Algebra and Multiple-valued Logic (Proc. Conf. Szeged, 1979). Colloq. Math. Soc. J. Bolyai, vol.28, 191–201, Amsterdam 1981.
D. Geiger, Closed systems of functions and predicates. Pacific J. Math.27, 95–100 (1968).
S. V. Jablonskii, Functional constructions in k-valued logic (Russian). Trudy Math. Inst. Steklov51, 5–142 (1958).
A. I. Mal'cev, A strengthening of the theorems of Slupecki and Jablonskii (Russian). Algebra i Logika6, no. 3, 61–75 (1967).
S. S. Marčenkov, Closed classes of self-dual functions in multiple-valued logic (Russian). Problemy Kibernetiki36, 5–22 (1979).
S. S. Marčenkov, J. Demetrovics andL. Hannák, Closed classes of self-dual functions inP 3 (Russian). Diskret. Analiz, to appear, English summary: Some remarks on the structure ofP 3, C.R. Math. Rep. Acad. Sci. Canada2, 215–219 (1980).
P. P. Pálfy, L. Szabó andÁ. Szendrei, Algebras with doubly transitive automorphism groups, in: Finite Algebra and Multiple-valued Logic (Proc. Conf. Szeged, 1979). Colloq. Math. Soc. J. Bolyai, vol.28, 521–535, Amsterdam 1981.
P. P.Pálfy, L.Szabó and Á.Szendrei, Automorphism groups and functional completeness. Algebra Universalis, to appear.
E. L.Post, The two-valued iterative systems of mathematical logic. Ann. Math. Studies5, Princeton 1941.
R.Pöschel und L. A.Kalužnin, Funktionen- und Relationenalgebren. Ein Kapitel der diskreten Mathematik, Math. Monographien B. 15, Berlin 1979; and Math. Reihe79, BaselStuttgart 1979.
I. G. Rosenberg, La structure des fonctions de plusieurs variables sur un ensemble fini. C.R. Acad. Sci. Paris, Ser. A.B.,260, 3817–3819 (1965).
I. G. Rosenberg, Über die funktionale Vollständigkeit in den mehrwertigen Logiken (Struktur der Funktionen von mehreren Veränderlichen auf endlichen Mengen). Rozpravy Česko- slovenské Akad. Věd. Řada Math. Přírod. Věd.80, 3–93 (1970).
I. G.Rosenberg, Completeness, closed classes and relations in multiple-valued logics, in: Proc. Intern. Sympos. on Multiple-valued Logics. pp. 1–26, Morgantown 1974.
I. G. Rosenberg, Functional completeness of single generated or surjective algebras, in: Finite Algebra and Multiple-valued Logic (Proc. Conf. Szeged, 1979). Colloq. Math. Soc. J. Bolyai, vol.28, 635–652, Amsterdam 1981.
A. Salomaa, On essential variables of functions especially in the algebra of logic. Ann. Acad. Sci. Fenn., Ser. AI Math.339, 3–11 (1963).
A. Salomaa, On infinitely generated sets of operations in finite algebras. Ann. Univ. Turku., Ser. AI74, 1–12 (1963).
L. Szabó andÁ. Szendrei, Almost all algebras with triply transitive automorphism groups are functionally complete. Acta. Sci. Math. (Szeged)41, 391–402 (1979).
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Szendrei, Á. Algebras of prime cardinality with a cyclic automorphism. Arch. Math 39, 417–427 (1982). https://doi.org/10.1007/BF01899542
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DOI: https://doi.org/10.1007/BF01899542