Lowness for Weakly 1-Generic and Kurtz-Random
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Date
2005-12-20
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Abstract
It is shown that a set is low for weakly 1-generic iff it has neither dnr nor hyperimmune Turing degree. As this notion is more general than being recursively traceable, this answers
negatively a recent question on the characterization of these sets. Furthermore, it is shown that every set which is low for weakly 1-generic is also low for Kurtz-random. In addition to this, it is shown that a set satisfies the notion ``low for diagonally non-recursive'' as introduced by Kjos-Hanssen and Nies iff it is recursive.