BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Athar Abdul-Quader (Purchase College) DTSTART:20230323T180000Z DTEND:20230323T190000Z DTSTAMP:20260423T052831Z UID:OLS/115 DESCRIPTION:Title: Ar ithmetic Saturation and Pathological Satisfaction\nby Athar Abdul-Quad er (Purchase College) as part of Online logic seminar\n\n\nAbstract\nA cla ssic result in models of arithmetic states that countable models of PA are recursively saturated if and only if they possess a "full satisfaction cl ass". A satisfaction class is a set of pairs (phi\, alpha)\, where phi is a code for a formula in the sense of the model\, and alpha is an assignmen t for that formula\, which extends the "standard" satisfaction relation\, and satisfies Tarksi's compositional rules for satisfaction. Recently\, th ere has been work on so-called pathological satisfaction classes: satisfac tion classes which exhibit certain pathologies\, like\, for example\, maki ng sentences of the form "(0 = 1) or (0 = 1) or ... or (0 =1)" of nonstand ard length true. We study these pathologies\, and find a surprising relati onship between the question of determining which sets can be defined using certain pathologies\, and a stronger notion of saturation\, arithmetic sa turation. This is joint work with Mateusz Łełyk\, based heavily on unpub lished work by Jim Schmerl.\n LOCATION:https://researchseminars.org/talk/OLS/115/ END:VEVENT END:VCALENDAR