Speaker: Steffen Lempp (University of Wisconsin-Madison)

Title: Separating Notions of Randomness (joint work with Bart Kastermans)

Abstract: The intuitive concept of randomness allows several possible
concise definitions, many of which have been shown to be inequivalent. We
discuss some of these notions and present a new separation result: Not every
"injectively partially computably random" (and thus in particular not every
"permutation partially computably random" set) is Martin-Löf random. This is
a partial result toward separating Martin-Löf randomness from
Kolmogorov-Loveland randomness, one of the main open questions in this area.
(See J. Miller/Nies, BSL, vol. 12, 2006, pp. 390-410, for more background on
this area.)