A function f is *diagonaly non-recursive* (DNR) if for every Turing index $e$, $f(e) \neq \Phi\_e(e)$.


A set is *strongly hyperhyperimmune* if there is no r.e. set of disjoint r.e. set intersecting it.


In their paper "A cohesive set which is not high", the authors claim that the jumps of the strongly hyperhyperimmune degrees coincide with the degrees of functions which are DNR relative to 0'.


How could it be possible knowing that there exists a $low\_2$ DNR relative to 0' and of course no jump can be $low\_2$ ?



Jump of strongly hyperhyperimmune degrees and DNR relative to 0'
Carl Jockusch and Frank Stephan. A cohesive set which is not high. Mathematical Logic Quarterly, 39:515-530, 1993. A corrective note (keeping the main results intact) appeared in the same journal, 43:569, 1997.


