BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Adam Přenosil (Vanderbilt University) DTSTART:20201029T180000Z DTEND:20201029T190000Z DTSTAMP:20260423T021155Z UID:OLS/33 DESCRIPTION:Title: Sem isimplicity\, Glivenko theorems\, and the excluded middle\nby Adam Př enosil (Vanderbilt University) as part of Online logic seminar\n\n\nAbstra ct\nThere are at least three different ways to obtain classical propositio nal logic from intuitionistic propositional logic. Firstly\, it is the ext ension of intuitionistic logic by the law of the excluded middle (LEM). Se condly\, it is related to intuitionistic logic by the double-negation tran slation of Glivenko. Finally\, the algebraic models of classical logic are precisely the semisimple algebraic models of intuitionistic logic (i.e. B oolean algebras are precisely the semisimple Heyting algebras). We show ho w to formulate the equivalence between the LEM and semisimplicity\, and be tween what we might call the Glivenko companion and the semisimple compani on of a logic\, at an appropriate level of generality. This equivalence wi ll subsume several existing Glivenko-like theorems\, as well as some new o nes. It also provides a useful technique for describing the semisimple sub varieties of a given variety of algebras. This is joint work with Tomáš Lávička\, building on previous work by James Raftery.\n LOCATION:https://researchseminars.org/talk/OLS/33/ END:VEVENT END:VCALENDAR