University Seminar- Computability, Complexity, and Algebraic Structure-Complexity of Orders on Groups

Time: Wednesday, November 13, 2:20 – 3:20pm

Place: Rome Hall, Room 352

Speaker:  Valentina Harizanov, GWU

Title: Complexity of Orders on Groups

Abstract:  A group is orderable if there is a linear ordering of its domain, which is both left- and right-invariant with respect to the group operation. There is a natural topology on the set of all group orders and this space is compact. A group is computable if its domain is computable and its operation is computable. A computable orderable group does not always have a computable order. On the other hand, there are groups with orders of every Turing degree. We will present how we construct such orders.