LOGIC BLOG 2013

Abstract. The 2013 logic blog has focussed on the following: 1. Higher randomness. Among others, the Borel complexity of Π11 ran-domness and higher weak 2 randomness is determined. 2. Reverse mathematics and its relationship to randomness. For in-stance, what is the strength of Jordan’s theorem in analysis? (His the-orem states that each function of bounded variation is the difference of two nondecreasing functions.) 3. Randomness and computable analysis. This focusses on the connec-tion of randomness of a real z and Lebesgue density of effectively closed sets at z. 4. Exploring similarity relations for Polish metric spaces, such as isom-etry, or having Gromov-Hausdorff distance 0. In particular their com-plexity was studied. 5. Various results connecting computability theory and randomness. Previous Logig Blogs from 2010 on can be found on Nies ’ web site