BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Corey Switzer (University of Vienna) DTSTART:20211022T130000Z DTEND:20211022T140000Z DTSTAMP:20260423T024455Z UID:VCU_ALPS/10 DESCRIPTION:Title: When is a set of reals "weird"?\nby Corey Switzer (University of Vie nna) as part of VCU ALPS (Analysis\, Logic\, and Physics Seminar)\n\n\nAbs tract\nThe axiom of choice guarantees the existence of "weird" or\n"pathol ogical" sets of real numbers and their relatives. Examples\ninclude well o rderings of the reals\, Lebesgue non-measurable sets and\nnon-principle ul trafilters (which can be coded as a set of reals). The\nguiding framework here is that such sets cannot be "defined" in the\nsense that they have no explicit definition\, which is why they do not\ncome up so often in analy sis and related fields. In this talk I will try\nto explain what this mean s more precisely as well as show that\, in some\nmodels of set theory\, "w eird" sets actually have rather nice\ndefinitions. Time permitting\, I wil l sketch some recent joint work with\nJeffrey Bergfalk and Vera Fischer sh owing that consistently many\npathological sets of reals can have very sim ple definitions all at the\nsame time.\n LOCATION:https://researchseminars.org/talk/VCU_ALPS/10/ END:VEVENT END:VCALENDAR