References
E. Post, “Introduction to a general theory of elementary propositions,” Amer. J. Math.,43, 163–185 (1921).
E. Post, Two-Valued Iterative Systems of Mathematical Logic, Princeton Univ. Press, Princeton (1941).
A. I. Malcev, “Iterative algebras and Post varieties,” Algebra i Logika,5, No. 2, 5–24 (1966).
A. I. Malcev, “Iterative Post Algebras [in Russian], Nauka, Novosibirsk, 1976.
A. I. Malcev, “On a certain extension of Slupecki's and Yablonskiî's theorems,” Algebra i Logika,6, No. 3, 61–75 (1967).
A. Goetz, “A. generalization of the direct product of universal algebras,” Colloq. Math.,22, 167–176 (1971).
S. V. Yablonskiî,” On functional completeness in three-valued calculus,” Dokl. Akad. Nauk SSSR,95, No. 6, 1152–1156 (1954).
S. V. Yablonskiî,” Functional constructions ink-valued logic,” Trudy Mat. Inst. Steklov. Akad. Nauk SSSR,51, 5–142 (1958).
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, “Ueber die funktionale Vollstaendigkeit in dem mehrvertigen Logiken von mehreren Veraendlichen auf endlichen Mengen,” Rozpravy Cs. Akademie Ved. Ser. Math. Nat. Sci.,80, 3–93 (1970).
B. A. Romov, “An algorithm for solving the completeness problem in the class of vector functional systems,” in: Mathematical Models of Complex Systems [in Russian], Inst. Kibernet. Akad. Nauk Ukrain. SSR, Kiev, 1973, pp. 151–155.
B. A. Romov, “On the subalgebra lattice of the direct product of Post algebras of finite degree,” in: Mathematical Models of Complex Systems [in Russian], Inst. Kibernet. Akad. Nauk Ukrain, SSR, Kiev, 1973, pp. 156–168.
B. A. Romov, “On completeness of logical functions on a square and in the systemP k xP l ,” Kibernetika, No. 4, 9–14 (1987).
B. A. Romov, “On a series of maximum subalgebras in the direct products of algebras of finite-valued logics,” Kibernetika, No. 3, 11–16 (1989).
B. A. Romov, “On functional completeness inP 2 xP k,” Kibernetika, No. 1, 1–8 (1991).
V. A. Taîmanov, “On the Cartesian powers ofP 2,” Dokl. Akad. Nauk SSSR,270, No. 6, 1327–1330 (1983).
S. S. Marchenkov, “On completeness inP 3 xP 3”, Diskretnaya Matematika,4, No.1, 126–145 (1992).
S. S. Marchenkov, “On Slupecki's classes inP k x … xP l ”, Diskretnaya Matematika,4, No. 3, 135–148 (1992).
I. G. Rosenberg, “Clones containing the direct square of a primal algebra”, in: Proceedings of the 12 International Symposium on Multiple-Valued Logic, CNAM Paris, 1982, pp. 30–34.
N. M. Ermolaeva and A. A. Muchnik, “Functionally closed 4-valued extensions of the Boolean algebra and corresponding logics,” in: Studies on Nonclassical Logics and Set Theory [in Russian], Nauka, Moscow, 1979, pp. 298–315.
J. Slupecki, “Kriterium pelnosci wielowartosciowich systemow logiki zdan,” in: Comptes Rendus des Seances de la Societe des Sciences et des Letters de Varsovie, Cl III, 1939,32, 102–128.
G. A. Burle, “Classes ofk-valued logic containing all functions of a certain variable,” Diskretnyî Analiz, No. 10, 3–7 (1967).
A. I. Malcev, “Some properties of cellular subalgebras of Post algebras and their basic cells”, Algebra i Logika11, No. 5, 571–587 (1972).
Additional information
Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 40, No. 1, pp. 102–112, January–February, 1999.
Rights and permissions
About this article
Cite this article
Malcev, I.A., Tugylbaeva, B.G. Products of iterative algebras. Sib Math J 40, 85–94 (1999). https://doi.org/10.1007/BF02674294
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02674294