{"id":1688,"date":"2012-11-07T15:30:09","date_gmt":"2012-11-07T15:30:09","guid":{"rendered":"http:\/\/www.illc.uva.nl\/lgc\/seminar\/?p=1688"},"modified":"2012-11-09T15:03:13","modified_gmt":"2012-11-09T15:03:13","slug":"lira-session-nick-bezhanishvili","status":"publish","type":"post","link":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/2012\/11\/lira-session-nick-bezhanishvili\/","title":{"rendered":"LIRa session: Nick Bezhanishvili"},"content":{"rendered":"<p>On November 15,\u00a0<strong>Nick\u00a0Bezhanishvili<\/strong> will give a LIRa talk.<br \/>\nEveryone is cordially invited!<\/p>\n<p><strong>Speaker:<\/strong> Nick\u00a0Bezhanishvili (Utrecht University)<br \/>\n<strong>Title:<\/strong> Extended dualities and Sahlqvist theorem for compact Hausdorff spaces<br \/>\n<strong>Room:<\/strong> Science Park 904, room B0.207<br \/>\n<strong>Time:<\/strong> Thursday, 15 November, 15:30-17:30<\/p>\n<p style=\"text-align: left;\"><strong>Abstract: <\/strong>A duality between modal algebras and modal spaces (descriptive Kripke frames) is of crucial importance\u00a0in modal logic. This duality is an extension of the celebrated Stone duality between Boolean algebras and Stone spaces.\u00a0This bridge between modal algebras and modal spaces has been instrumental in investigations of wide range of\u00a0phenomena in modal logic and led to a resolution of many open problems in the area.<\/p>\n<p>In this talk I will present an extension of this duality beyond Stone spaces. In particular, I will introduce modal compact Hausdorff\u00a0spaces (MKH-spaces), which generalize modal spaces. I will also define modal compact regular frames and modal de Vries algebras and\u00a0show that these algebras provide dualities \u00a0for MKH-spaces that extend the duality between modal spaces and modal algebras.\u00a0As the first step in the logical treatment of these dualities, a version of Sahlqvist correspondence for the positive modal language will be given.\u00a0I will also discuss a number of open problems that concern logical aspects of these extended dualities.<\/p>\n<p>This is joint work with Guram Bezhanishvili and John Harding.<\/p>\n<p style=\"text-align: justify;\">&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>On November 15,\u00a0Nick\u00a0Bezhanishvili will give a LIRa talk.<br \/>\nEveryone is cordially invited!<br \/>\nSpeaker: Nick\u00a0Bezhanishvili (Utrecht University)<br \/>\nTitle: Extended dualities and Sahlqvist theorem for compact Hausdorff spaces<br \/>\nRoom: Science Park 904, room B0.207<br \/>\nTime: Thursday, 15 November, 15:30-17:30<br \/>\nAbstract: A duality between modal algebras and modal spaces (descriptive Kripke frames) is of crucial importance\u00a0in modal logic. This duality is an extension of [&#8230;]<\/p>\n","protected":false},"author":11,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14,4],"tags":[],"class_list":["post-1688","post","type-post","status-publish","format-standard","hentry","category-all","category-events"],"_links":{"self":[{"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/posts\/1688","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/comments?post=1688"}],"version-history":[{"count":12,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/posts\/1688\/revisions"}],"predecessor-version":[{"id":1693,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/posts\/1688\/revisions\/1693"}],"wp:attachment":[{"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/media?parent=1688"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/categories?post=1688"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/tags?post=1688"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}