BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sarah Reitzes (University of Chicago) DTSTART:20211025T203000Z DTEND:20211025T210000Z DTSTAMP:20260423T005745Z UID:CTA/64 DESCRIPTION:Title: Com paring induction and bounding principles over RCA0 and RCA*0\nby Sarah Reitzes (University of Chicago) as part of Computability theory and appli cations\n\n\nAbstract\nIn this talk\, I will discuss joint work with Damir D. Dzhafarov and Denis R. Hirschfeldt\, and more recent work following th at line of research. Our work centers on the characterization of reduction s between Π12 problems P and Q in terms of winning strategies in certain games. These characterizations were originally introduced by Hirschfeldt a nd Jockusch in [1]. I will discuss extensions and generalizations of these characterizations\, including a certain notion of compactness that allows us\, for strategies satisfying particular conditions\, to bound the numbe r of moves it takes to win. This bound is independent of the instance of t he problem P being considered. This allows us to develop the idea of Weihr auch and generalized Weihrauch reduction over some base theory. Here\, we will focus on the base theory RCA0 and the weaker system RCA*0. In this ta lk\, I will explore these notions of reduction among various principles\, including bounding and induction principles. I will present a metatheorem that allows us to obtain many nonreductions between these principles. \n\n [1] D. R. Hirschfeldt and C. G. Jockusch\, Jr.: On notions of computabilit y-theoretic reduction between Π12 principles. Journal of Mathematical Log ic 16 (1650002)\, 59 pp. (2016)\n LOCATION:https://researchseminars.org/talk/CTA/64/ END:VEVENT END:VCALENDAR