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Lattice of Mal’tsev theories. (English. Russian original) Zbl 0588.08004

Algebra Logic 23, 203-209 (1984); translation from Algebra Logika 23, No. 3, 296-304 (1984).
The paper continues the investigations initiated in [Algebra Logika 22, 693-706 (1983; Zbl 0575.08004)]. The author studies Mal’cev theories and proves that they form a complete lattice (under inclusion) which is dually isomorphic to the lattice of nonempty special Mal’cev classes (or \(S_{\delta}\)-classes).
Reviewer: L.Esakia

MSC:

08B05 Equational logic, Mal’tsev conditions
08B15 Lattices of varieties

Citations:

Zbl 0575.08004
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References:

[1] D. M. Smirnov, ”Mal’tsev conditions and representability of varieties,” Algebra Logika,22, No. 6, 693–706 (1983). · Zbl 0575.08004
[2] J. T. Baldwin and J. Berman, ”A model theoretic approach to Mal’cev conditions,” J. Symbolic Logic,42, No. 2, 277–288 (1977). · Zbl 0412.03016 · doi:10.2307/2272131
[3] B. Jónsson, ”Congruence varieties,” Alg. Univ.,10, No. 3, 355–394 (1980). · Zbl 0438.08003 · doi:10.1007/BF02482916
[4] W. Taylor, ”Characterising Mal’cev conditions,” Alg. Univ.,3, No. 3, 351–397 (1973). · Zbl 0304.08003 · doi:10.1007/BF02945141
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