Saturday, October 18, 201411:40 amNERDS: New England Recursion & Definability SeminarAssumption College, Worcester, MA

# The degree spectra of orders on a computable Abelian group

## Caleb Martin

### University of Connecticut

For any computable abelian group, the collection of possible linear orderings on the group can be represented as a Π^{0}_{1} class. However, not all Π^{0}_{1} classes can occur in this way, and we investigate the possible Turing degrees of their members. First, we describe the connection between orders for a group and bases for the group. Additionally, we extend a previously known result regarding the Turing degrees not represented in the space of orders of some group.

Caleb Martin is a graduate student in computability theory at the University of Connecticut, working with Reed Solomon.