Date of Completion

4-24-2015

Embargo Period

4-24-2015

Keywords

logic, computability theory, recursion theory, computable structure theory, low for isomorphism

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

We explore the notion of lowness for isomorphism as restricted to various classes and subclasses of structures. We present results for equivalence structures, scattered linear orders, the non-scattered linear orders known as shuffle sums, and for various restrictions of these classes, with an emphasis on examining which properties, in general terms, of these structures play a role in which results and how changes to the various constructions affect the resulting structures. Finally, we present partial information on the relationships between the various types of results and their associated subclasses of structures, with notes on how we might expect these results to generalize.

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