Hi,
Any other thoughts, suggestions, or references would be appreciated.
In L. S. Completions of \mu-algebras. APAL, 154(1):27-50, May 2008. I studied the problem of the completeness of the modal mu-calculus from an finitary algebraic point of view. In that paper some categorical ideas, mainly from W. Tholen, Pro-categories and multiadjoint functors, Canad. J. Math. 36 (1) (1984) 144–155. play the relevant role. The challenge is to prove that in free modal \mu-algebras, the relation \mu.f = \bigvee_{n>=0} f^n(\bot) holds -- where \mu.f, the least fixpoint of f, is axiomatized by equational implications and free modal \mu-algebras are not known to be complete. Best, Luigi -- Luigi Santocanale LIF/CMI Marseille Tél: 04 91 11 35 74 http://www.cmi.univ-mrs.fr/~lsantoca/ Fax: 04 91 11 36 02