Lowness Properties and Approximations of the Jump

Authors:
Santiago Figueira;André Nies;Frank Stephan
Affiliations:
Department of Computer Science, FCEyN, University of Buenos Aires, Argentina;Department of Computer Science, University of Auckland, New Zealand;Departments of Computer Science and Mathematics, National University of Singapore, Singapore
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2006

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Abstract

We study and compare two combinatorial lowness notions: strong jump-traceability and well-approximability of the jump, by strengthening the notion of jump-traceability and @w-r.e. for sets of natural numbers. We prove that there is a strongly jump-traceable set which is not computable, and that if A^' is well-approximable then A is strongly jump-traceable. For r.e. sets, the converse holds as well. We characterize jump-traceability and the corresponding strong variant in terms of Kolmogorov complexity, and we investigate other properties of these lowness notions.