Time: Wednesday, March 22, 2:20-3:20pm
Place: Monroe Hall, Room 250
Speaker: Meng-Che (Turbo) Ho, California State University, Northridge
Title: Describing finitely generated groups
Abstract: Computable structure theory aims to study the complexity of mathematical structures. In particular, the descriptive complexity of a structure can be described by the index set or Scott sentences of the structure. In general, these complexities can be arbitrarily high in the hyperarithmetical hierarchy. However, Knight and Saraph observed that finitely generated structures will always have a Sigma_3 Scott sentence.
In this talk, we will focus on finitely generated groups. It turns out that this Sigma_3 Scott sentence is not optimal for many finitely generated groups as they admit d-Sigma_2 Scott sentences. On the other hand, there are finitely generated groups for which this Scott sentence is optimal. We will discuss characterizations of this dividing line.
Part of the talk is based on joint work with Matthew Harrison-Trainor.