BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dragan Masulovic (University of Novi Sad) DTSTART:20220208T200000Z DTEND:20220208T210000Z DTSTAMP:20260423T004759Z UID:PALS/25 DESCRIPTION:Title: Du al Ramsey properties for classes of algebras\nby Dragan Masulovic (Uni versity of Novi Sad) as part of PALS Panglobal Algebra and Logic Seminar\n \n\nAbstract\nAlmost any reasonable class of finite relational structures has the Ramsey property or a precompact Ramsey expansion. In contrast to t hat\, the list of classes of finite algebras with the precompact Ramsey ex pansion is surprisingly short. In this talk we show that any nontrivial va riety (that is\, equationally defined class of algebras) enjoys various du al Ramsey properties. We develop a completely new set of strategies that r ely on the fact that left adjoints preserve the dual Ramsey property\, and then treat classes of algebras as Eilenberg-Moore categories for a monad. We show that finite algebras in any nontrivial variety have finite dual s mall Ramsey degrees\, and that every finite algebra has finite dual big Ra msey degree in the free algebra on countably many free generators. As usua l\, these come as consequences of ordered versions of the statements.\n LOCATION:https://researchseminars.org/talk/PALS/25/ END:VEVENT END:VCALENDAR