Logic Blog 2020

Abstract

This year's blog has focused on the connections of group theory with logic and algorithms. The first post is on automata presentable groups. Then there are several posts related to topological groups, for instance Ivanov and Majcher showing that extreme amenability of closed subgroups of $S_\infty$ is a Borel property. One post due to Harrison-Trainor and Nies reviews notes by Segal on pseudofinite groups, and attempts an effective version. About 25 percent is on computability and randomness, in particular equivalence of reducibilities weaker than Turing on the K-trivials by Greenberg, Nies and Turetsky, and the effective SMB theorem in the quantum setting by Nies and Tomamichel.