Invitation to the Logic Seminar at the National University of Singapore

Date: Thursday, 25 February 2016, 17:00 hrs

Room: S17#04-06, Department of Mathematics, NUS

Speaker: Andre Nies, The University of Auckland

Title: The complexity of isomorphism between profinite groups

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

A topological group G is profinite if it is compact and totally

disconnected. Equivalently, G is the inverse limit of a surjective

system of finite groups carrying the discrete topology. An example is

the additive group of 2-adic integers.

We discuss how to represent a countably based profinite group as a

point in a Polish space. Thereafter, we study the complexity of their

isomorphism using the theory of Borel reducibility in descriptive set

theory. For topologically finitely generated groups this complexity is

the same as the one of identity for reals. In general, it is the same

as the complexity of isomorphism for countable graphs.