Reals which compute little
André Nies · Cambridge University Press eBooks · 2017
We investigate combinatorial lowness properties of sets of natural numbers (reals). The real A is super-low if A # # ,andA is jump-traceable if the values of (e) can be e#ectively 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 #-r.e. sets. Finally we prove that, for any low r.e. set B, there is is a K-trivial set A ##T B. 1