Kurt Gödel Research Center

2014 seminar talk: Orders on groups, their spaces, and complexity

Talk held by Valentina Harizanov (George Washington University, Washington, D.C., USA) at the KGRC seminar on 2014-03-06.

Abstract

We investigate properties of orders on groups, which respect the algebraic structure. There is a natural topology on the (nonempty) set of such orders, and this space is compact even for a structure with a single binary operation (non necessarily a semigroup). We study the spaces as well as computability-theoretic complexity of orders on groups, both abelian and nonabelian. While not all computable orderable groups have computable orders, many familiar groups contain orders in every Turing degree above a specific degree.