BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alberto Marcone (Università di Udine) DTSTART:20200915T130000Z DTEND:20200915T140000Z DTSTAMP:20260423T005718Z UID:CTA/22 DESCRIPTION:Title: The higher levels of the Weihrauch lattice\nby Alberto Marcone (Universit à di Udine) as part of Computability theory and applications\n\n\nAbstrac t\nThe classification of mathematical problems in the Weihrauch lattice is a line of research that blossomed in the last few years. Initially this a pproach dealt mainly with statements which are provable in ACA_0 and showe d that usually Weihrauch reducibility is more fine-grained than reverse ma thematics.\n\nIn the last few years the study of multi-valued functions ar ising from statements laying at higher levels (such as ATR_0 and Pi^1_1-CA _0) of the reverse mathematics spectrum started as well. The multi-valued functions studied so far include those arising from the perfect tree theor em\, comparability of well-orders\, determinacy of open and clopen games\ , König’s duality theorem\, various forms of choice\, the open and clop en Ramsey theorem and the Cantor-Bendixson theorem.\n\nAt this level often a single theorem naturally leads to several multi-valued functions of dif ferent Weihrauch degree\, depending on how the theorem is "read" from a co mputability viewpoint. A case in point is the perfect tree theorem: it can be read as the request to produce a perfect subtree of a tree with uncoun tably many paths\, or as the request to list all paths of a tree which doe s not contain a perfect subtree. Similarly\, the clopen Ramsey theorem lea ds to the multi-valued function that associates to every clopen subset of [N]^N an infinite homogeneous set on either side\, and to the multi-valued function producing for each clopen subset which has an infinite homogeneo us sets on one side a homogeneous set on that side. Similar functions can be defined similarly starting from the open Ramsey theorem.\n\nIn this tal k I discuss some of these results\, emphasizing recent joint work with my students Vittorio Cipriani and Manlio Valenti.\n LOCATION:https://researchseminars.org/talk/CTA/22/ END:VEVENT END:VCALENDAR