Priestley duality for some subalgebra lattices

Studia Logica 56 (1-2):133 - 149 (1996)
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Priestley duality can be used to study subalgebras of Heyting algebras and related structures. The dual concept is that of congruence on the dual space and the congruence lattice of a Heyting space is dually isomorphic to the subalgebra lattice of the dual algebra. In this paper we continue our investigation of the congruence lattice of a Heyting space that was undertaken in [10], [8] and [12]. Our main result is a characterization of the modularity of this lattice (Theorem 2.12). Partial results about its complementedness are also given, and among other things a characterization of those finite Heyting algebras with a complemented subalgebra lattice (Theorem 3.5).



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Modal logic and classical logic.Johan van Benthem - 1983 - Atlantic Highlands, N.J.: Distributed in the U.S.A. by Humanities Press.

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