LIRa session: Nick Bezhanishvili

On November 15, Nick Bezhanishvili will give a LIRa talk.
Everyone is cordially invited!

Speaker: Nick Bezhanishvili (Utrecht University)
Title: Extended dualities and Sahlqvist theorem for compact Hausdorff spaces
Room: Science Park 904, room B0.207
Time: Thursday, 15 November, 15:30-17:30

Abstract: A duality between modal algebras and modal spaces (descriptive Kripke frames) is of crucial importance in modal logic. This duality is an extension of the celebrated Stone duality between Boolean algebras and Stone spaces. This bridge between modal algebras and modal spaces has been instrumental in investigations of wide range of phenomena in modal logic and led to a resolution of many open problems in the area.

In this talk I will present an extension of this duality beyond Stone spaces. In particular, I will introduce modal compact Hausdorff spaces (MKH-spaces), which generalize modal spaces. I will also define modal compact regular frames and modal de Vries algebras and show that these algebras provide dualities  for MKH-spaces that extend the duality between modal spaces and modal algebras. As the first step in the logical treatment of these dualities, a version of Sahlqvist correspondence for the positive modal language will be given. I will also discuss a number of open problems that concern logical aspects of these extended dualities.

This is joint work with Guram Bezhanishvili and John Harding.