Physical Sciences and Mathematics Commons^™

Reducibility, Degree Spectra, And Lowness In Algebraic Structures, Rebecca M. Steiner

Dissertations, Theses, and Capstone Projects

This dissertation addresses questions in computable structure theory, which is a branch of mathematical logic hybridizing computability theory and the study of familiar mathematical structures. We focus on algebraic structures, which are standard topics of discussion among model theorists. The structures examined here are fields, graphs, trees under a predecessor function, and Boolean algebras.

For a computable field F, the splitting set S_F of F is the set of polynomials in F[X] which factor over F, and the root set R_F of F is the set of polynomials in F[X] which have a root in F …