  The top right of the diagram shows the recursively enumerable (r.e.) problems; this includes r.e.-complete problems such as the halting problem (Halt). On the left is the set of co-r.e. problems including the co-r.e.-complete problem \(\overline{{\rm Halt}}\) -- the set of Turing Machines that never halt on a given input.  We mentioned at the end of Section 2.3 that the intersection of the set of r.e problems and the set of co-r.e problems is equal to the set of Recursive problems.  The set of Primitive Recursive problems is a strict subset of the Recursive problems.