Logic Seminar
Itai Ben Yaacov
Université Claude Bernard Lyon 1, Institut Camille Jordan
Independence and mean widths
Abstract: A relation between two sets X and Y is said to be dependent if it does
not shatter arbitrarily large finite subsets of X. Similarly, a
function X x Y -> [0,1] is dependent if for every e > 0 it does not
e-shatter arbitrarily large finite subsets of X. A characterisation of
dependent functions in terms of the growth rate of the mean width of a
family of associated convex compacts is essential to proving that the
expectation of a random family of uniformly dependent functions is again
dependent. Model theoretically, this means that the Keisler randomisation of a
dependent theory is again dependent, answering a question of Pillay and
allowing a more direct approach to the study of Keisler measure in
(classical) dependent theories.
there shall be tea at 4pm, talk at 4:20. Some of us will go out for dinner afterwards.
Monday February 11, 2008 at 4:00 PM in SEO 427