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Finite pseudo-Boolean and topological Boolean algebras not having an independent basis of quasiidentities

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Literature cited

  1. V. P. Belkin, "Quasiidentities of finite rings and lattices," Algebra Logika,17, No. 3, 246–259 (1978).

    Article  Google Scholar 

  2. V. A. Gorbunov, "Coverings in lattices of quasivarieties and independent axiomatizability," Algebra Logika,16, No. 4, 507–548 (1977).

    Google Scholar 

  3. G. Grätzer, General Lattice Theory, Birkhauser, Basel-Stuttgart; Academic Press, New York (1978).

    Google Scholar 

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

    Google Scholar 

  5. A. Yu. Ol'shanskii, "Conditional identities in finite groups," Sib. Mat. Zh.,15, No. 6, 1409–1413 (1974).

    Google Scholar 

  6. H. Rasiowa and R. Sikorski, The Mathematics of Metamathematics, 3rd edn., PWN, Warsaw (1970).

    Google Scholar 

  7. V. V. Rybakov, "Bases of quasiidentities of finite modal algebras," Algebra Logika,21, No. 2, 219–227 (1982).

    Article  Google Scholar 

  8. M. P. Tropin, "On bases of quasiidentities of finite distributive p-algebras," Algebra Logika,26, No. 4, 456–480 (1987).

    Google Scholar 

  9. M. P. Tropin, "On quasiidentities of finite pseudo-Boolean and topological Boolean algebras," 8th All-Union Conf. on Mathematical Logic, Moscow (1986), p. 195.

  10. M. E. Adams, "Implicational classes of pseudocomplemented distributive lattices," J. London Math. Soc.,13, 381–384 (1976).

    Google Scholar 

  11. W. J. Blok and D. Pigozzi, "On the structure of varieties with equationally definable principal congruences. I," Algebra Univ.,15, 195–227 (1982).

    Google Scholar 

  12. W. Dziobiak, "Concerning axiomatizability of the quasivariety generated by a finite Heyting or topological Boolean algebra," Stud. Logica,41, No. 4, 415–428 (1981).

    Article  Google Scholar 

  13. R. I. Goldblatt, "Metamathematics of modal logic. II," Rep. Math. Logic,7, 21–53 (1976).

    Google Scholar 

  14. G. Grätzer, Lattice Theory. First Concepts and Distributive Lattices, Freeman, San Francisco (1971).

    Google Scholar 

  15. D. H. J. de Jongh and A. S. Troelstra, "On the connection of partially ordered sets with some pseudo-Boolean algebras," Indag. Math.,28, 317–329 (1966).

    Google Scholar 

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

    Google Scholar 

  17. R. McKenzie, "Equational bases for lattice theories," Math. Scand.,27, 24–38 (1970).

    Google Scholar 

  18. H. A. Priestley, "Representations of distributive lattices by means of ordered Stone spaces," Bull. London Math. Soc.,2, No. 5, 186–190 (1970).

    Google Scholar 

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Translated from Algebra i Logika, Vol. 27, No. 1, pp. 79–99, January–February, 1988.

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Tropin, M.P. Finite pseudo-Boolean and topological Boolean algebras not having an independent basis of quasiidentities. Algebra and Logic 27, 57–69 (1988). https://doi.org/10.1007/BF01978303

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