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Covers in lattices of quasivarieties and independent axiomatizability

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Literature Cited

  1. A. A. Akataev and D. M. Smirnov, "Lattices of subvarieties of varieties of algebras," Algebra Logika,7, No. 1, 5–25 (1968).

    Google Scholar 

  2. V. P. Belkin, "Quasi-identities of certain finite algebras," Mat. Zametki,22, No. 3, 335–338 (1977).

    Google Scholar 

  3. A. I. Budkin and V. A. Gorbunov, "On the theory of quasivarieties of algebraic systems," Algebra Logika,14, No. 2, 123–142 (1975).

    Google Scholar 

  4. V. A. Gorbunov, "Lattices of quasivarieties," Algebra Logika,15, No. 4, 436–457 (1976).

    Google Scholar 

  5. V. I. Igoshin, "Quasivarieties of lattices," Mat. Zametki,16, No. 1, 49–56 (1974).

    Google Scholar 

  6. Kourovka Notebook (Unsolved Problems of Group Theory) [in Russian], Novosibirsk (1976).

  7. A. I. Mal'tsev, Algebraic Systems [in Russian], Nauka (1970).

  8. A. I. Mal'tsev, "Some questions on the boundary between algebra and mathematical logic," in: Proceedings of the International Congress of Mathematicians, Moscow, 1966, Mir (1968), pp. 217–231.

  9. A. I. Mal'tsev, "Universally axiomatizable subclasses of locally finite classes of models," Sib. Mat. Zh.,8, No. 5, 1005–1014 (1967).

    Google Scholar 

  10. A. N. Trakhtman, "A variety of semigroups having no irreducible basis of identities," Mat. Zametki,21, No. 6, 865–871 (1977).

    Google Scholar 

  11. A. N. Trakhtman, "Covering elements in the lattice of varieties of algebras," Mat. Zametki,15, No. 2, 174–177 (1974).

    Google Scholar 

  12. P. Crawley and R. P. Dilworth, Algebraic Theory of Lattices, Prentice-Hall, Englewood Cliffs, New Jersey (1973).

    Google Scholar 

  13. A. Day, "Splitting algebras and a weak notion of projectivity," Algebra Univ.,5, 153–162 (1975).

    Google Scholar 

  14. J. Jezek, "Intervals in the lattice of varieties," Algebra Univ.,6, 147–158 (1976).

    Google Scholar 

  15. B. Jónsson, "Algebras whose congruence lattices are distributive," Math. Scand.,21, 110–121 (1967).

    Google Scholar 

  16. B. Jónsson, "Equational classes of lattices," Math. Scand.,22, 187–196 (1968).

    Google Scholar 

  17. A. Kostinsky, "Projective lattices and bounded homomorphisms," Pacific J. Math.,40, 111–119 (1972).

    Google Scholar 

  18. A. I. Mal'tsev (Malcev), The Metamathematics of Algebraic Systems (Collected Papers: 1936–1967), North-Holland, Amsterdam-London (1971).

    Google Scholar 

  19. A. Monteiro, "Axiomes indépendants pour les algèbres de Brouwer," Revista Union Math. Argentina,27, 149–160 (1955).

    Google Scholar 

  20. W. Nemitz and T. Whaley, "Varieties of implicative semilattices. II," Pacific J. Math.,45, No. 1, 303–311 (1973).

    Google Scholar 

  21. A. Tarski, "Equational logic and equational theories of algebras," in: Contributions to Mathematical Logic, North-Holland, Amsterdam-London (1968), pp. 275–288.

    Google Scholar 

  22. I. Reznikoff, "Tout ensemble de formules de la logique classique est équivalent à un ensemble indépendant," C. R. Hebdomadaire Seances Acad. Sci.,260, No. 1, 2385–2388 (1965).

    Google Scholar 

  23. A. Shafaat, "On implicational compactness," Canad. J. Math.,26, No. 3, 761–768 (1974).

    Google Scholar 

  24. A. Shafaat, "Subcartesian products of finitely many finite algebras," Proc. Am. Math. Soc.,26, No. 3, 401–404 (1970).

    Google Scholar 

  25. V. Slavik, "Note on subquasivarieties of some varieties of lattices," Comment. Math. Carol.,16, No. 1, 173–181 (1975).

    Google Scholar 

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Authors
  1. V. A. Gorbunov
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Translated from Algebra i Logika, Vol. 16, No. 5, pp. 507–548, September–October, 1977.

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Gorbunov, V.A. Covers in lattices of quasivarieties and independent axiomatizability. Algebra and Logic 16, 340–369 (1977). https://doi.org/10.1007/BF01669475

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