PP-2002-10: Duals of subdirectly irreducible modal algebras

PP-2002-10: Venema, Yde (2002) Duals of subdirectly irreducible modal algebras. [Report]

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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. These
characterizations involve a special binary \emph{quasi-reachability}
relation on the dual structure; we call a point $u$ a quasi-root of
the dual structure if every ultrafilter is quasi-reachable from $u$.
We prove that a boolean algebra with operators is simple iff every
point in the dual structure is a quasi-root; and that it is
subdirectly irreducible iff the collection of quasi-roots has measure
nonzero in the Stone topology on the dual structure.

Item Type:	Report
Report Nr:	PP-2002-10
Series Name:	Prepublication (PP) Series
Year:	2002
Uncontrolled Keywords:	boolean algebras with operators, modal logic, subdirectly irreducible algebras, simple algebras, duality
Subjects:	Logic
Date Deposited:	12 Oct 2016 14:36
Last Modified:	12 Oct 2016 14:36
URI:	https://eprints.illc.uva.nl/id/eprint/74

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