Logic Blog 2013

André Nies

Published 2014-03-23, updated 2014-06-19Version 2

The 2013 logic blog has focussed on the following: 1. Higher randomness. Among others, the Borel complexity of $\Pi^1_1$ randomness and higher weak 2 randomness is determined. 2. Reverse mathematics and its relationship to randomness. For instance, what is the strength of Jordan's theorem in analysis? (His theorem states that each function of bounded variation is the difference of two nondecreasing functions.) 3. Randomness and computable analysis. This focusses on the connection 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 isometry, or having Gromov-Hausdorff distance $0$. In particular their complexity was studied. 5. Various results connecting computability theory and randomness.