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Medientyp:
E-Artikel
Titel:
A Dual Characterization of Subdirectly Irreducible BAOs
Beteiligte:
Venema, Yde
Erschienen:
Kluwer Academic Publishers, 2004
Erschienen in:Studia Logica: An International Journal for Symbolic Logic
Sprache:
Englisch
ISSN:
0039-3215;
1572-8730
Entstehung:
Anmerkungen:
Beschreibung:
<p>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.</p>