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Abstract:

A modal lattice is a bounded distributive lattice endowed with a unary operator which preserves the join-operation and the smallest element. In this paper we consider the variety CH of modal lattices that is generated by the totally ordered modal lattices and we characterize the lattice of subvarieties of CH. We also give an equational basis for each subvariety of CH.

Registro:

Documento: Artículo
Título:Equational Classes of Totally Ordered Modal Lattices
Autor:Petrovich, A.
Filiación:Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Palabras clave:Modal lattices; Priestley relations; Priestley spaces
Año:1999
Volumen:16
Número:1
Página de inicio:1
Página de fin:17
DOI: http://dx.doi.org/10.1023/A:1006259631226
Título revista:Order
Título revista abreviado:Order
ISSN:01678094
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01678094_v16_n1_p1_Petrovich

Referencias:

  • Blok, W.J., The lattice of modal logics: An algebraic investigation (1980) J.S.L., 45 (2), pp. 221-236
  • Blok, W.J., The lattice of varieties of modal algebras is not strongly atomic (1980) Algebra Universalis, 11, pp. 285-294
  • Blok, W.J., Pretabular varieties of modal algebras (1980) Studia Logica, 39, pp. 101-124
  • Makinson, D.C., Some embedding theorems for modal logic (1971) Notre Dame J. Formal Logic, 12, pp. 252-254
  • Cignoli, R., Lafalce, S., Petrovich, A., Remarks on Priestley duality for distributive lattices (1991) Order, 8, pp. 299-315
  • Goldblatt, R., Varieties of complex algebras (1989) Ann. Pure Appl. Logic, 44 (3), pp. 153-301
  • Makinson, D., Aspectos de la lógica modal (1971) Notas de Lógica Matemática, 28. , Instituto de Matemática, Universidad Nacional del Sur, Bahía Blanca
  • Petrovich, A., Distributive lattices with an operator (1996) Studia Logica, 56, pp. 205-224
  • Priestley, H.A., Representation of distributive lattices by means of ordered Stone spaces (1970) Bull. London Math. Soc., 2, pp. 186-190
  • Priestley, H.A., Ordered topological spaces and the representation of distributive lattices (1972) Proc. London Math. Soc., 2 (4), pp. 507-530
  • Priestley, H.A., Stone lattices: A topological approach (1974) Fund. Math., 84, pp. 127-143

Citas:

---------- APA ----------
(1999) . Equational Classes of Totally Ordered Modal Lattices. Order, 16(1), 1-17.
http://dx.doi.org/10.1023/A:1006259631226
---------- CHICAGO ----------
Petrovich, A. "Equational Classes of Totally Ordered Modal Lattices" . Order 16, no. 1 (1999) : 1-17.
http://dx.doi.org/10.1023/A:1006259631226
---------- MLA ----------
Petrovich, A. "Equational Classes of Totally Ordered Modal Lattices" . Order, vol. 16, no. 1, 1999, pp. 1-17.
http://dx.doi.org/10.1023/A:1006259631226
---------- VANCOUVER ----------
Petrovich, A. Equational Classes of Totally Ordered Modal Lattices. Order. 1999;16(1):1-17.
http://dx.doi.org/10.1023/A:1006259631226