Dr. Luca Motto Ros, Freiburg, Vorstellungsvortrag:
On the invariant universality property
Time and place
Thursday, 6.6.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Abstract
The notion of Borel reducibility has been introduced as a tool for measuring the\ntopological complexity of analytic equivalence relations and quasi-orders, an abstract class of\nobjects which includes many relations from various areas of mathematics such as: isomorphism and\n(algebraic) embeddability between countable structures from model theory, homeomorphism and\ntopological embeddability between continua from general topology, isometry and isometric\nembeddability between Polish spaces from analysis, linear isometry and linear isometric\nembeddability between separable Banach spaces from functional analysis, and many others.\nIntuitively, an analytic quasi-order as above is called invariantly universal if it contains in a\nnatural way a Borel-isomorphic copy of any other analytic quasi-order. In this talk, building on\nprevious work of Louveau and Rosendal we will show that most of the analytic quasi-orders which\nare sufficiently complicated (that is: Borel-complete) are in fact invariantly universal. For\nexample, one can show that for every analytic quasi-order R there is a Borel collection C of\nseparable Banach spaces closed under linear isometry such that the relation of linear isometric\nembeddability on C is Borel-isomorphic to R.\n