Logic Blog 2020

TL;DR

The Logic Blog 2020 explores the interplay between group theory, logic, and algorithms, covering topics from automata groups to topological groups, pseudofinite groups, and computability, highlighting recent advances and open problems.

Contribution

It provides a comprehensive overview of recent research connecting group theory with logic and algorithms, including new results on automata groups, topological properties, and computability aspects.

Findings

Extreme amenability of certain groups is a Borel property

Effective versions of pseudofinite groups are explored

Equivalence of reducibilities on K-trivials is analyzed

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.