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The class of Kleene algebras satisfying an interpolation property and Nelson algebras

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References

  1. R. Balbes andP. Dwinger,Distributive Lattices, University of Missouri Press, Columbia, Missouri, 1974.

    Google Scholar 

  2. D. Brignole,Equational Characterization of Nelson Algebras, Notre Dame J. Formal Logic,10 (1969), 285–297. Reproduced in Notas de Lógica Matemática No 9, Universidad Nacional del Sur, Bahía Blanca, 1974.

    Google Scholar 

  3. D. Brignole andA. Monteiro,Caractérisation des Algébres de Nelson par des Egalités. I, II, Proc. Japan Acad.,43 (1967), 279–285. Reproduced in Notas de Lógica Matemática No 20, Universidad Nacional del Sur, Bahía Blanca, 1964.

    Google Scholar 

  4. R. Cignoli,Boolean Elements in Lukasiewicz Algebras. I, Proc. Japan Acad.,41 (1965), 670–675. Reproduced in Notas de Lógica Matemática No 23, Universidad Nacional del Sur, Bahía Blanca, 1974.

    Google Scholar 

  5. R. Cignoli,Coproducts in the Categories of Kleene and Three-Valued Lukasiewicz Algebras, Studia Logica,38 (1979), 237–245.

    Google Scholar 

  6. R. Cignoli andM. S. de Gallego,The Lattice Structure of Some Lukasiewicz Algebras, Algebra Universalis,13 (1985), 315–328.

    Google Scholar 

  7. R. Cignoli andM. S. de Gallego,Dualities for some De Morgan Algebras with Operators and Lukasiewicz Algebras, J. Austral. Math. Soc. (Series A),34 (1983), 377–393.

    Google Scholar 

  8. W. H. Cornish andP. R. Fowler,Coproducts of De Morgan Algebras, Bull. Austral. Math. Soc.,16 (1977), 1–13.

    Google Scholar 

  9. W. H. Cornish andP. R. Fowler,Coproducts of Kleene Algebras, J. Austral. Math. Soc. (Series A),27 (1979), 209–220.

    Google Scholar 

  10. M. Fidel,An Algebraic Study of a Propositional System of Nelson, Mathematical Logic: Proceedings of the First Brazilian Conference (A. I. Arruda, N. C. A. da Costa and R. Chuaqui, Editors), Lecture Notes in Pure and Applied Mathematics Vol. 39, M. Dekker Inc., New York, 1978, pp. 99–117.

    Google Scholar 

  11. J. Kalman,Lattices with involution, Trans. Amer. Math. Soc.,87 (1958), 485–491.

    Google Scholar 

  12. S. MacLane,Categories for the Working Mathematician, Graduate Texts in Mathematics, Vol. 5, Springer-Verlag, N. York, Heidelberg, Berlin, 1971.

    Google Scholar 

  13. A. Monteiro,Construction des Algébres de Nelson Finies, Bull. Acad. Pol. Sci.,11 (1963), 359–362. Reproduced in Notas de Lógica Matemática No 15, Universidad Nacional del Sur, Bahía Blanca, 1964.

    Google Scholar 

  14. A. Monteiro,Algebras de Nelson Semi-Simples (Abstract), Rev. Unión Mat. Argentina,21 (1963), 145–146.

    Google Scholar 

  15. A. Monteiro,Construction des Algèbres de Lukasiewicz Trivalentes Dans les Algèbres de Boole Monadiques. I, Math. Japonicae,12 (1967), 1–23. Reproduced in Notas de Lógica Matemática No 11, Universidad Nacional del Sur, Bahía Blanca, 1974.

    Google Scholar 

  16. A. Monteiro,Les Eléments Réguliers d'un N-Lattice, Anaes Acad. Brasil. Ciênc.,52 (1980), 653–656.

    Google Scholar 

  17. H. A. Priestley,Representation of Distributive Lattices by Means of Ordered Stone Spaces, Bull. London Math. Soc.,2 (1970), 186–190.

    Google Scholar 

  18. H. A. Priestley,Ordered Topological Spaces and the Representation of Distributive Lattices, Proc. London Math. Soc. (3),24 (1972), 507–530.

    Google Scholar 

  19. H. A. Priestley,Stone Lattices: a Topological Approach, Fund. Math.,84 (1974), 127–143.

    Google Scholar 

  20. H. A. Priestley,The Construction of Spaces Dual to Pseudocomplemented Distributive Lattices, Quart. J. Math., Ser. 2,26 (1975), 215–228.

    Google Scholar 

  21. H. A. Priestley,Ordered Sets Duality for Distributive Lattices, Ann. Discrete Math.,23 (1984), 39–60.

    Google Scholar 

  22. H. Rasiowa,N-Lattices and Constructive Logic with Strong Negation, Fund. Math.,46 (1958), 61–80.

    Google Scholar 

  23. H. Rasiowa,An Algebraic Approach to non-Classical Logics, North-Holland, Amsterdam 1974.

    Google Scholar 

  24. A. Urquhart,Distributive Lattices with a Dual Homomorphic Operation, Studia Logica,38 (1979), 201–209.

    Google Scholar 

  25. D. Vakarelov,Notes on N-Lattices and Constructive Logic with Strong Negation,34 (1977), 109–125.

    Google Scholar 

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Cignoli, R. The class of Kleene algebras satisfying an interpolation property and Nelson algebras. Algebra Universalis 23, 262–292 (1986). https://doi.org/10.1007/BF01230621

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