A dual characterization of subdirectly irreducible BAOs

Studia Logica 77 (1):105 - 115 (2004)
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Abstract

We give a characterization of the simple, and of the subdirectly irreducible boolean algebras with operators (including modal algebras), in terms of the dual descriptive frame, or, topological relational structure. These characterizations involve a special binary topo-reachability relation on the dual structure; we call a point u a topo-root of the dual structure if every ultrafilter is topo-reachable from u. We prove that a boolean algebra with operators is simple iff every point in the dual structure is a topo-root; and that it is subdirectly irreducible iff the collection of topo-roots is open and non-empty in the Stone topology on the dual structure iff this collection has non-empty interior in that topology.

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Yde Venema
University of Amsterdam

Citations of this work

Stable canonical rules.Guram Bezhanishvili, Nick Bezhanishvili & Rosalie Iemhoff - 2016 - Journal of Symbolic Logic 81 (1):284-315.
Stable modal logics.Guram Bezhanishvili, Nick Bezhanishvili & Julia Ilin - 2018 - Review of Symbolic Logic 11 (3):436-469.

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