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Quasiidentities of two-element algebras. (English. Russian original) Zbl 0535.08006
Algebra Logic 22, 83-88 (1983); translation from Algebra Logika 22, 121-127 (1983).
The purpose of this paper is to give a new, shorter proof to an earlier result of the author, namely: Every two-element algebra of a finite similarity type generates a minimal, finitely based quasivariety.
Reviewer: J.Ježek

08C15 Quasivarieties
08B05 Equational logic, Mal’tsev conditions
Full Text: DOI EuDML
[1] V. A. Gorbunov, ”Coverings in lattices of quasivarieties and independent axiomatizability,” Algebra Logika,10, No. 5, 507–548 (1977). · Zbl 0403.08009
[2] V. A. Gorbunov, ”Quasiidentities of finite algebras,” in: 15th All-Union Algebraic Conference, Part 2 [in Russian] (1979), p. 42.
[3] A. I. Mal’tsev, Algebraic Systems [in Russian], Nauka (1970).
[4] A. I. Mal’tsev, ”To the general theory of algebraic systems,” Mat. Sb.,35, No. 1, 3–20 (1954).
[5] K. A. Baker, ”Finite equational bases for finite algebras in a congruence-distributive equational class,” Adv. Math.,24, 207–243 (1977). · Zbl 0356.08006
[6] J. Baldwin and J. Berman, ”The number of subdirectly irreducible algebras in a variety,” Algebra Univ.,5, 379–389 (1975). · Zbl 0348.08002 · doi:10.1007/BF02485271
[7] J. Berman, ”A proof of Lyndon’s finite bases theorem,” Discrete Math.,29, 229–233 (1980). · Zbl 0449.08004 · doi:10.1016/0012-365X(80)90150-8
[8] D. M. Clark and P. H. Krauss, ”Varieties generated by para primal algebras,” Algebra Univ.,7, 93–114 (1977). · Zbl 0435.08004 · doi:10.1007/BF02485419
[9] G. Grätzer, Universal Algebra, 2nd edition, Springer-Verlag (1978).
[10] B. Jónsson, ”Algebras whose congruence lattices are distributive,” Math. Scand.,21, 110–121 (1967). · Zbl 0167.28401
[11] R. C. Lyndon, ”Identities in two-valued calculi,” Trans. Am. Math. Soc.,71, No. 3, 457–465 (1951). · Zbl 0044.00201 · doi:10.1090/S0002-9947-1951-0044470-3
[12] R. McKenzie, ”Para primal varieties: A study of finite axiomatizability of definable principal congruences in locally finite varieties,” Algebra Univ.,8, 336–348 (1978). · Zbl 0383.08008 · doi:10.1007/BF02485404
[13] D. Pigozzi, ”Minimal locally finite varieties are not finitely axiomatizable,” Algebra Univ.,9, 374–390 (1979). · Zbl 0426.08003 · doi:10.1007/BF02488049
[14] E. Post, Two-Valued Iterative Systemsof Mathematical Locig, Princeton Univ. Press (1941).
[15] H. Werner, Discriminator Algebras, Akademie-Verlag, Berlin (1978).
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