Date of Completion
5-8-2015
Embargo Period
5-8-2015
Major Advisor
David Reed Solomon
Associate Advisor
Damir Dzhafarov
Associate Advisor
Stephen Flood
Field of Study
Mathematics
Degree
Doctor of Philosophy
Open Access
Open Access
Abstract
Ordered abelian groups are studied from the viewpoint of computability theory. In particular, we examine the possible complexity of orders on a computable abelian group. The space of orders on such a group may be represented in a natural way as the set of infinite paths through a computable tree, but not all such sets can occur in this way. We describe the connection between the complexity of a basis for a group and an order for the group, and completely characterize the degree spectra of the set of bases for a group. We describe some restrictions on the possible degree spectra of the space of orders, including a connection to algorithmic randomness.
Recommended Citation
Martin, Caleb J., "Computability Theory and Ordered Groups" (2015). Doctoral Dissertations. 766.
https://digitalcommons.lib.uconn.edu/dissertations/766