Abstract
As we have seen, the K-trivial sets form a class of “extremely low” sets, properly contained within the class of superlow sets and closed under join. The study of K-triviality has led to an increased interest in notions of computability-theoretic weakness. In particular, various forms of traceability have played important roles. In this chapter we study the notion of strong jump traceability introduced by Figueira, Nies, and Stephan [147] and later studied by Cholak, Downey, and Greenberg [65], among others, and explore its connections with K-triviality and other randomnesstheoretic notions.
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© 2010 Springer Science+Business Media, LLC
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Downey, R.G., Hirschfeldt, D.R. (2010). Strong Jump Traceability. In: Algorithmic Randomness and Complexity. Theory and Applications of Computability. Springer, New York, NY. https://doi.org/10.1007/978-0-387-68441-3_14
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DOI: https://doi.org/10.1007/978-0-387-68441-3_14
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Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-95567-4
Online ISBN: 978-0-387-68441-3
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