Strong Jump Traceability

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.