BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexi Block Gorman (University of Illinois Urbana-Champaign) DTSTART:20210527T180000Z DTEND:20210527T190000Z DTSTAMP:20260423T035731Z UID:OLS/54 DESCRIPTION:Title: Def inability on the Reals from Büchi Automata\nby Alexi Block Gorman (Un iversity of Illinois Urbana-Champaign) as part of Online logic seminar\n\n \nAbstract\nBüchi automata are the natural analogue of finite automata in the context of infinite strings (indexed by the natural numbers) on a fin ite alphabet. We say a subset X of the reals is r-regular if there is a B üchi automaton that accepts (one of) the base-r representations of every element in X\, and rejects the base-r representations of each element in i ts complement. These sets often exhibit fractal-like behavior—e.g.\, the Cantor set is 3-regular. There are remarkable connections in logic to Bü chi automata\, particularly in model theory. In this talk\, I will give a characterization of when the expansion of the real ordered additive group by a predicate for a closed r-regular subset of [0\,1] is model-theoretica lly tame (d-minimal\, NIP\, NTP2). Moreover\, I will discuss how this coi ncides with geometric tameness\, namely trivial fractal dimension. This w ill include a discussion of how the properties of definable sets vary depe nding on the properties of the Büchi automaton that recognizes the predic ate subset.\n LOCATION:https://researchseminars.org/talk/OLS/54/ END:VEVENT END:VCALENDAR