Traceability of the Jump and its Connection to Algorithmic Randomness

(Abstract)

In this talk I will discuss various notions on the traceability of a set.

Traceability allows us to obtain different guesses for the given set in some effective manner. Sets which are traceable also exhibit lowness properties, both in the classical sense and in connection with algorithmic randomness.

In particular I will consider the interesting case of the jump traceable sets. This notion has been shown recently to be intricately linked with the K-trivial reals, which are reals exhibiting anti-random properties. I will also introduce a very strong variant of jump traceability, called the hyper jump traceable sets. These sets form the first known subclass of the K-trivial reals having no promptly simple members. Some other surprising properties of this class is also discussed.