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| Title: | Use-Bounded Strong Reducibilities |
| Authors: | Belanger, David |
| Keywords: | computability
degree 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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