Use-Bounded Strong Reducibilities
David Belanger · UWSpace (University of Waterloo) · 2009
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.