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On the approximation of the Boolean powers by Cartesian powers. (English) Zbl 0844.08002

Summary: On the basis of the Mal’tsev-Cleave theorem on quasi-universal formulas, it is proved that a number of properties of congruences, tolerances, quasiorders can be transported from finite Cartesian powers of algebraic systems to any Boolean powers.

MSC:

08A05 Structure theory of algebraic structures
08A30 Subalgebras, congruence relations
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References:

[1] Foster A. L.: Functional completeness in the small. Algebraic structure theorems and identities. Math. Ann., v. 143, N 1, 1961, 29-53. · Zbl 0095.02201 · doi:10.1007/BF01351890
[2] Burris S.: Boolean powers. Alg. Univ., v. 5, N 3, 1975, 341-360. · Zbl 0328.08003 · doi:10.1007/BF02485268
[3] Pinus A. G.: Boolean constructions in universal algebra. Kluwer Academ. Publish., Dordrecht-Boston-London, 1993. · Zbl 0792.08001
[4] Pinus A. G.: On the covers in epimorphism skeletons of varreties of algebras. Algebra and logic, v. 27, N 3, 1988, 316-326) · Zbl 0666.08004
[5] Malcev A. I.: The model correspondences. Izvestia AN SSSR, ser. math., v. 23, N 3, 1959, 313-336)
[6] Cleave I. P.: Local properties of systems. J. London Math. Soc. (1), v. 44, N 1, 1969, 121-130, Addendum., J. London. Math. Soc. (2), v. 1, N 2, 1969, p. 384. · Zbl 0169.00701 · doi:10.1112/jlms/s1-44.1.121
[7] Kargapolov M. I., Merzljakov, Ju. I.: Fundaments of the theory of groups. Nauka, Moscow, 1972) · Zbl 0549.20001
[8] Chajda I.: Algebraic theory of tolerance relations. UP Olomouc, Monography series., 1991. · Zbl 0747.08001
[9] Pinus A. G., Chajda I.: Quasiorders on the universal algebras. Algebra and logic, v. 32, N 3, 1993) · Zbl 0824.08002 · doi:10.1007/BF02261695
[10] Fraser G. A., Horn A.: Congruence relations in direct products. Proc. Amer. Math. Soc., v. 26, N 2, 1970, 390-394. · Zbl 0241.08004 · doi:10.2307/2037345
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