Abstract
We study the distinctions between Q-reducibility and m-reducibility on computably enumerable sets. We construct a noncomputable m-incomplete computably enumerable set B such that all computably enumerable sets A ≤QB satisfy A ≤mB. We prove that for every noncomputable computably enumerable set A there exists a computably enumerable set B such that A ≤QB but A ≰mB. We prove that for every simple set B there exists a computably enumerable set A such that A ≤QB but A ≰mB. The last result implies in particular that the Q-degree of every simple set contains infinitely many computably enumerable m-degrees.
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