BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Patrick Lutz (UCLA) DTSTART:20230119T190000Z DTEND:20230119T200000Z DTSTAMP:20260423T035932Z UID:OLS/109 DESCRIPTION:Title: Th e Solecki dichotomy and the Posner Robinson theorem\nby Patrick Lutz ( UCLA) as part of Online logic seminar\n\n\nAbstract\nThe Solecki dichotomy in descriptive set theory\, roughly stated\, says that every Borel functi on on the real numbers is either a countable union of partial continuous f unctions or at least as complicated as the Turing jump. The Posner-Robinso n theorem in computability theory\, again roughly stated\, says that every non-computable real looks like 0' relative to some oracle. Superficially\ , these theorems look similar: both roughly say that some object is either simple or as complicated as the jump. However\, it is not immediately app arent whether this similarity is more than superficial. If nothing else\, the Solecki dichotomy is about third order objects—functions on the real numbers—while the Posner-Robinson theorem is about second order objects —individual real numbers. We will show that there is a genuine mathemati cal connection between the two theorems by showing that the Posner-Robinso n theorem plus determinacy can be used to give a short proof of a slightly weakened version of the Solecki dichotomy\, and vice-versa.\n LOCATION:https://researchseminars.org/talk/OLS/109/ END:VEVENT END:VCALENDAR