Previous |  Up |  Next

Article

Keywords:
Boolean algebras; modal algebras; Boolean spaces with relations
Summary:
In this paper we introduce the class of Boolean algebras with an operator between the algebra and the set of ideals of the algebra. This is a generalization of the Boolean algebras with operators. We prove that there exists a duality between these algebras and the Boolean spaces with a certain relation. We also give some applications of this duality.
References:
[1] Brink C., Rewitzky I. M.: Finite-cofinite program relations. Log. J. IGPL 7 (1999), 153–172. MR 1682045
[2] Bosangue M., Kwiatkowska M.: Re-interpreting the modal $\mu $-calculus. Modal Logic and Process Algebra: A Bisimulation Perspective. A. Ponse, M. de Rijke, Y. Venema (eds.), CSLI Lectures Notes, Stanford, CA, 1995. MR 1375698
[3] Goldblatt R.: Mathematics of Modality. CSLI Lectures Notes, Stanford, CA, 1993. MR 1317099 | Zbl 0942.03516
[4] Goldblatt R.: Saturation and the Hennessy-Milner Property. Modal Logic and Process Algebra: A Bisimulation Perspective, A. Ponse, M. de Rijke, Y. Venema (eds.), CSLI Lectures Notes, Stanford, CA, 1995. MR 1375698
[5] Jónsson B., Tarski A.: Boolean algebras with Operators, Part I. Amer. J. Math. 73 (1951), 891–939. MR 0044502
[6] Koppelberg S.: Topological duality. Handbook of Boolean Algebras, J. D. Monk, R. Bonnet (eds.) vol. 1, North-Holland, Amsterdam, 1989, pp. 95–126. MR 0991565
[7] Sambin G., Vaccaro V.: Topology and duality in modal logic. Ann. Pure Appl. Logic 37 (1988), 249–296. MR 0934369
Partner of
EuDML logo