algebra universalis

, 15:195 | Cite as

On the structure of varieties with equationally definable principal congruences I

  • W. J. Blok
  • D. Pigozzi


Distributive Lattice Congruence Lattice Subdirect Product Heyting Algebra Discriminator Variety 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [1]
    R. Balbes and Ph.Dwinger,Distributive Lattices. University of Missouri Press, 1974.Google Scholar
  2. [2]
    K. A. Baker,Equational axioms for classes of Heyting algebras. Algebra Universalis6 (1976), p. 105–120.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    —,Finite equational bases for finite algebras in a congruence-distributive equational class. Advances in Math.24 (1977), p. 207–243.MathSciNetzbMATHGoogle Scholar
  4. [4]
    —,Primitive satisfaction and equational problems for lattices and other algebras. T.A.M.S.190 (1974), p. 125–150.CrossRefzbMATHGoogle Scholar
  5. [5]
    J. Berman,Distributive lattices with an additional operation. Aequationes Math.16 (1977), p. 165–171.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    C. Bernardi,On the equational class of diagnoziable algebras. Studia Logica34 (1975), p. 321–331.MathSciNetCrossRefGoogle Scholar
  7. [7]
    W. J. Blok,Varieties of interior algebras. Dissertation, University of Amsterdam, 1976.Google Scholar
  8. [8]
    —,The lattice of modal logics, an algebraic investigation, J.S.L.45 (1980), p. 221–236.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    W. J. Blok and Ph.Dwinger,Equational classes of closure algebras. I. Ind. Math.37 (1975), p. 189–198.MathSciNetGoogle Scholar
  10. [10]
    W. J. Blok andD. Pigozzi,The deduction theorem in algebraic logic. Manuscript.Google Scholar
  11. [11]
    S. Bulman-Fleming andH. Werner,Equational compactness in quasi-primal varieties, Algebra Universalis7 (1977), p. 33–46.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    S. Burris andH. Werner,Sheaf constructions and their elementary properties. T.A.M.S.248 (1979), p. 269–309.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    A. Diego,Sur les algèbres de Hilbert. Collection de Logique Mathematique, Series A, No. 21, Paris 1966.Google Scholar
  14. [14]
    R. Franci,Filtra and ideal classes of universal algebras. Quaderni dell'Istituto di Matematica dell'Universita di Siena (1976).Google Scholar
  15. [15]
    E. Fried, G. Grätzer, andR. Qackenbush,Uniform congruence schemes. Algebra Universalis10 (1980), p. 176–189.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    E. Fried andE. W. Kiss,Connection between the congruence lattices and polynomial properties. Preprint.Google Scholar
  17. [17]
    E. Fried andA. F. Pixley,The dual discriminator function in universal algebra. Acta Univ. Szeged41 (1979), p. 83–100.MathSciNetzbMATHGoogle Scholar
  18. [18]
    G. Grätzer,Universal Algebra. Springer-Verlag, 1979.Google Scholar
  19. [19]
    T. Hecht andT. Katrinák,Principal congruences of p-algebras and double p-algebras, Proc. Amer. Math. Soc.58 (1976), p. 25–31.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    L. Henkin, J. D. Monk andA. Tarski,Cylindric algebras, Part I. North-Holland Publishing Company, Amsterdam 1971.zbMATHGoogle Scholar
  21. [21]
    V. A. Jankov,The relationship between deducibility in the intuitionistic propositional calculus and finite implicational structures. Sov. Math. Dokl.4 (1963), p.-1203–1204.Google Scholar
  22. [22]
    B. Jónsson,Algebras whose congruence lattices are distributive. Math. Scand.21 (1967), p. 110–121.MathSciNetzbMATHGoogle Scholar
  23. [23]
    B. Jónsson andA. Tarski,Boolean algebras with operators. Part I. Amer. J. Math.73 (1951) p. 891–939.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    —,Boolean algebras with operators. Part II. Amer. J. Math.74 (1952), p. 127–162.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    T. Katrinák,The structure of distributive double p-algebras. Regularity and congruences. Algebra Universalis3 (1973), p. 238–246.MathSciNetzbMATHCrossRefGoogle Scholar
  26. [26]
    P. Köhler,Brouwerian semilattices. Math. Institut, Justus Liebig Universität, Giessen.Google Scholar
  27. [27]
    P. Köhler andD. Pigozzi,Varieties with equationally definable principal congruences. Algebra Universalis,11 (1980), p. 213–219.MathSciNetzbMATHCrossRefGoogle Scholar
  28. [28]
    H. Lakser,Principal congruences of pseudo-complemented distributive lattices. Proc. Amer. Math. Soc.37 (1973), p. 32–36.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    —,The structure of pseudo-complemented distributive lattices, I. T.A.M.S.,156 (1971), p. 335–342.MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    K. B. Lee,Equational classes of distributive pseudo-complemented lattices Canad. J. Math.22 (1970), p. 881–891.MathSciNetzbMATHGoogle Scholar
  31. [31]
    J. Łos,Quelques remarques, theorèmes et problèmes sur les classes définissables d'algèbres. Mathematical interpretation of formal systems. North-Holland Publ. Co. Amsterdam, 1955, p. 98–113.Google Scholar
  32. [32]
    S. MacLane,Categories for the Working Mathematician. Springer-Verlag, 1971.Google Scholar
  33. [33]
    R. Magari,Varietà a quozienti filtrali. Ann. Univ. Ferrara, Sez. VII14 (1969), 5–20.MathSciNetzbMATHGoogle Scholar
  34. [34]
    —,Representation and duality theory for diagonizable algebras. Studia Logica34 (1975), p. 305–313.MathSciNetCrossRefGoogle Scholar
  35. [35]
    R. McKenzie,Equational bases and non-modular lattice varieties. T.A.M.S.174 (1972), p. 1–43.MathSciNetCrossRefGoogle Scholar
  36. [36]
    W. C. Nemitz,Implicative semilattices, T.A.M.S.,117 (1965), p. 128–142.MathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    Semi-Boolean lattices, Notre Dame J. of Formal Logic10 (1969), p. 128–142.MathSciNetCrossRefGoogle Scholar
  38. [38]
    H. Rasiowa,An algebraic approach to non-classical logics. North-Holland Publ. Co., Amsterdam, 1974.zbMATHGoogle Scholar
  39. [39]
    W. Rautenberg,Der Verband der normalen und verzweigten Modallogiken. Math. Z.156 (1977), p. 123–140.MathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    W. Rautenberg,Klassische und Nichtklassische Aussagenlogik. Vieweg, 1979.Google Scholar
  41. [41]
    H. P. Sankappanavar,A characterization of principal congruences of De Morgan algebras and its applications. Math Logic in Latin America, Proc. IV Latin Amer. Symp. Math. Logic, Santiago 1978, p. 341–349. North-Holland Pub. Co., Amsterdam, 1980.Google Scholar
  42. [42]
    A. Tarski,Contributions to the theory of model, III. Ind. Math.17 (1955), p. 56–64.MathSciNetGoogle Scholar
  43. [43]
    H. Ursini,Intuitionistic diagonizable algebras. Algebra Universalis,9 (1979), p. 229–237.MathSciNetzbMATHCrossRefGoogle Scholar
  44. [44]
    H. Werner,Discriminator algebras. Studien zur Algebra und ihre Anwendungen 6, Akademie Verlag, Berlin (1978).zbMATHGoogle Scholar

Copyright information

© Birkhäuser Verlag 1982

Authors and Affiliations

  • W. J. Blok
    • 1
    • 2
  • D. Pigozzi
    • 1
    • 2
  1. 1.Simon Fraser UniversityBurnabyCanada
  2. 2.Iowa State UniversityAmesU.S.A.

Personalised recommendations