BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:George Metcalfe (University of Bern) DTSTART:20220428T180000Z DTEND:20220428T190000Z DTSTAMP:20260423T035748Z UID:OLS/88 DESCRIPTION:Title: Fro m ordered groups to ordered monoids and back again\nby George Metcalfe (University of Bern) as part of Online logic seminar\n\n\nAbstract\n(Join t work with Almudena Colacito\, Nikolaos Galatos\, and Simon Santschi)\n\n Removing the inverse operation from any lattice-ordered group (l-group)\, such as the ordered additive group of integers\, produces a distributive l attice-ordered monoid (l-monoid)\, but it is not the case that every distr ibutive l-monoid admits a group structure. In particular\, every l-group e mbeds into an l-group of automorphisms of some chain and is either trivial or infinite\, whereas every distributive l-monoid embeds into a possibly finite l-monoid of endomorphisms of some chain.\n\nIn this talk\, we will see that inverse-free abelian l-groups generate only a proper (infinitely based) subvariety of the variety of commutative distributive l-monoids\, b ut inverse-free l-groups generate the whole variety of distributive l-mono ids. We will also see that the validity of an l-group equation can be redu ced to the validity of a (constructible) finite set of l-monoid equations\ , yielding --- since the variety of distributive l-monoids has the finite model property — an alternative proof of the decidability of the equatio nal theory of l-groups.\n LOCATION:https://researchseminars.org/talk/OLS/88/ END:VEVENT END:VCALENDAR