Yde Venema:


        	Subdirect irreducibility (a frame perspective)


                                  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 general frame.
These characterizations involve a special binary *quasi-reachability*
relation on the dual structure; we call a point a quasi-root of the dual
structure if every ultrafilter is quasi-reachable from it.
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.