26 April 2017, Algebra|Coalgebra Seminar, George Metcalfe

Ordering conditions for groups provide useful tools for the study of various relationships between group theory, universal algebra, topology, and logic. In this talk, I will describe a new “algorithmic” ordering condition for extending partial orders on groups to total orders. I will then show how this condition can be used to show that extending a finite subset of a free group to a total order corresponds to checking validity of a certain inequation in the class of totally ordered groups. As a direct consequence, we obtain a new proof that free groups are orderable.