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:20260404T143401Z UID:OLS/7 DESCRIPTION:Title: Limited-information strategies in Banach-Mazur games\nby William Br ian (UNC Charlotte) as part of Online logic seminar\n\n\nAbstract\nThe Ban ach-Mazur game is an infinite-length game played on a topological space X\ , in which two players take turns choosing members of an infinite decreasi ng sequence of open sets\, the first player trying to ensure that the inte rsection of this sequence is empty\, and the second that it is not. A limi ted-information strategy for one of the players is a game plan that\, on a ny given move\, depends on only a small part of the game's history. In thi s talk we will discuss Telgársky's conjecture\, which asserts roughly tha t 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 ga me's history in a significant way. Recently\, it was shown that this conje cture fails in models of set theory satisfying GCH + □. In such models i t is always possible for one player to code all information concerning a g ame's history into a small piece of it. We will discuss these so-called co ding strategies\, why assuming GCH + □ makes them work so well\, and wha t can go wrong in other models of set theory.\n LOCATION:https://stable.researchseminars.org/talk/OLS/7/ END:VEVENT END:VCALENDAR