On strongly jump traceable reals

Annals of Pure and Applied Logic 154 (1):51-69 (2008)
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Abstract

In this paper we show that there is no minimal bound for jump traceability. In particular, there is no single order function such that strong jump traceability is equivalent to jump traceability for that order. The uniformity of the proof method allows us to adapt the technique to showing that the index set of the c.e. strongly jump traceables is image-complete

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10.1016/j.apal.2007.11.014

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Citations of this work

Benign cost functions and lowness properties.Noam Greenberg & André Nies - 2011 - Journal of Symbolic Logic 76 (1):289 - 312.
Strong Jump-Traceability.Noam Greenberg & Dan Turetsky - 2018 - Bulletin of Symbolic Logic 24 (2):147-164.
Computing from projections of random points.Noam Greenberg, Joseph S. Miller & André Nies - 2019 - Journal of Mathematical Logic 20 (1):1950014.

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References found in this work

[Omnibus Review].Rod Downey - 1997 - Journal of Symbolic Logic 62 (3):1048-1055.
Computational randomness and lowness.Sebastiaan A. Terwijn & Domenico Zambella - 2001 - Journal of Symbolic Logic 66 (3):1199-1205.
Working below a low2 recursively enumerably degree.Richard A. Shore & Theodore A. Slaman - 1990 - Archive for Mathematical Logic 29 (3):201-211.
Lowness properties and approximations of the jump.Santiago Figueira, André Nies & Frank Stephan - 2008 - Annals of Pure and Applied Logic 152 (1):51-66.
Computational complexity, speedable and levelable sets.Robert I. Soare - 1977 - Journal of Symbolic Logic 42 (4):545-563.

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