An Introduction to Randomness

Mark Carney, University of Leeds. Part of the proofs, constructions and computations seminar series.

The study of randomness has developed considerably in the latter half of the 20th, and into the first half of the 21st century.  We will give an overview of some of the more interesting results that relate to logic in particular. We will present Martin-Löf Randomness (MLR) by means of MLR-tests and then relate these definitions to Pi^0_1-classes, in particular a theorem due to Kucera, as well as some results from Reverse Mathematics.