McKinsey Algebras and Topological Models of S4.1

Abstract

The aim of this paper is to show that every topological space gives rise to a wealth of topological models of the modal logic S4.1. The construction of these models is based on the fact that every space defines a Boolean closure algebra (to be called a McKinsey algebra) that neatly reflects the structure of the modal system S4.1. It is shown that the class of topological models based on McKinsey algebras contains a canonical model that can be used to prove a completeness theorem for S4.1. Further, it is shown that the McKinsey algebra MKX of a space X endoewed with an alpha-topologiy satisfies Esakia's GRZ axiom.

Author's Profile

Thomas Mormann
Ludwig Maximilians Universit√§t, M√ľnchen (PhD)

Analytics

Added to PP
2012-10-19

Downloads
638 (#26,345)

6 months
131 (#31,800)

Historical graph of downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.
How can I increase my downloads?