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# Lowness Properties and Approximations of the Jump

@article{Figueira2006LownessPA, title={Lowness Properties and Approximations of the Jump}, author={Santiago Figueira and Andr{\'e} Nies and Frank Stephan}, journal={Electr. Notes Theor. Comput. Sci.}, year={2006}, volume={143}, pages={45-57} }

- Published 2006 in Electr. Notes Theor. Comput. Sci.
DOI:10.1016/j.entcs.2005.05.025

We study and compare two combinatorial lowness notions: strong jump-traceability and wellapproximability of the jump, by strengthening the notion of jump-traceability and ω-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… CONTINUE READING