Please use this identifier to cite or link to this item: http://hdl.handle.net/10012/4564

 Title: Use-Bounded Strong Reducibilities Authors: Belanger, David Keywords: computabilitydegree structure Approved Date: 20-Aug-2009 Date Submitted: 2009 Abstract: We study the degree structures of the strong reducibilities $(\leq_{ibT})$ and $(\leq_{cl})$, as well as $(\leq_{rK})$ and $(\leq_{wtt})$. We show that any noncomputable c.e. set is part of a uniformly c.e. copy of $(\BQ,\leq)$ in the c.e. cl-degrees within a single wtt-degree; that there exist uncountable chains in each of the degree structures in question; and that any countable partially-ordered set can be embedded into the cl-degrees, and any finite partially-ordered set can be embedded into the ibT-degrees. We also offer new proofs of results of Barmpalias and Lewis-Barmpalias concerning the non-existence of cl-maximal sets. Program: Pure Mathematics Department: Pure Mathematics Degree: Master of Mathematics URI: http://hdl.handle.net/10012/4564 Appears in Collections: Electronic Theses and Dissertations (UW) Faculty of Mathematics Theses and Dissertations

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