Abstract
We introduce the class of bounded distributive lattices with two operators, Δ and ∇, the first between the lattice and the set of its ideals, and the second between the lattice and the set of its filters. The results presented can be understood as a generalization of the results obtained by S. Celani.
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References
Balbes, R. and Dwinger, P.: Distributive Lattices, University of Missouri Press, 1974.
Celani, S. A.: Quasi-modal algebras, Math. Bohemica 126(4) (2001), 721–736.
Celani, S. A. and Jansana, R.: Priestley duality, a Sahlqvist theorem and a Goldblatt–Thomason theorem for positive modal logic, L. J. IGLP 6 (1999), 683–715.
Cignoli, R., Lafalce, S. and Petrovich, A.: Remarks on Priestley duality for distributive lattices, Order 8 (1991), 299–315.
Gehrke, M. and Jónsson, B.: Bounded distributive lattices with operators, Math. Japonica 40(2) (1994), 207–215.
Goldblatt, R.: Varieties of complex algebras, Ann. Pure Appl. Logic 44 (1989), 173–242.
Petrovich, A.: Distributive lattices with an operator, Studia Logica 56 (1996), 205–224.
Priestley, H. A.: Representation of distributive lattices by means of ordered Stone spaces, Bull. London Math. Soc. 2 (1970), 186–190.
Priestley, H. A.: Ordered topological spaces and the representation of distributive lattices, Proc. London Math. Soc. 3 (1972), 507–530.
Priestley, H. A.: Stone lattices a topological approach, Fund. Math. 84 (1974), 127–143.
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Jorge Castro: The work of the first author was partially supported by Grant BFM2001-3329 of D.G.I.C.Y.T. of Spain.
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Castro, J., Celani, S. Quasi-Modal Lattices. Order 21, 107–129 (2004). https://doi.org/10.1007/s11083-004-6449-3
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DOI: https://doi.org/10.1007/s11083-004-6449-3