Lowness for weakly 1-generic and kurtz-random

Authors:
Frank Stephan;Liang Yu
Affiliations:
School of Computing and Department of Mathematics, National University of Singapore, Singapore;Department of Mathematics, National University of Singapore, Singapore
Venue:
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Year:
2006

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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.