BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:William Brian (UNC Charlotte) DTSTART:20200604T180000Z DTEND:20200604T190000Z DTSTAMP:20260423T035612Z UID:OLS/7 DESCRIPTION:Title: Limi ted-information strategies in Banach-Mazur games\nby William Brian (UN C Charlotte) as part of Online logic seminar\n\n\nAbstract\nThe Banach-Maz ur game is an infinite-length game played on a topological space X\, in wh ich two players take turns choosing members of an infinite decreasing sequ ence of open sets\, the first player trying to ensure that the intersectio n of this sequence is empty\, and the second that it is not. A limited-inf ormation strategy for one of the players is a game plan that\, on any give n move\, depends on only a small part of the game's history. In this talk we will discuss Telgársky's conjecture\, which asserts roughly that there must be topological spaces where winning strategies for the Banach Mazur game cannot be too limited\, but must rely on large parts of the game's hi story in a significant way. Recently\, it was shown that this conjecture f ails in models of set theory satisfying GCH + □. In such models it is al ways possible for one player to code all information concerning a game's h istory into a small piece of it. We will discuss these so-called coding st rategies\, why assuming GCH + □ makes them work so well\, and what can g o wrong in other models of set theory.\n LOCATION:https://researchseminars.org/talk/OLS/7/ END:VEVENT END:VCALENDAR