Reals which compute little [chapter]

Andre Nies, Zoe Chatzidakis, Peter Koepke, Wolfram Pohlers
Logic Colloquium '02  
We investigate combinatorial lowness properties of sets of natural numbers (reals). The real A is super-low if A ≤tt ∅ , and A is jump-traceable if the values of {e} A (e) can be effectively approximated in a sense to be specified. We investigate those properties, in particular showing that super-lowness and jump-traceability coincide within the r.e. sets but none of the properties implies the other within the ω-r.e. sets. Finally we prove that, for any low r.e. set B, there is is a K-trivial set A ≤T B.
doi:10.1017/9781316755723.012 fatcat:wiwlegscvna5dn6e7vqdp755wq