A Hierarchy of Computably Enumerable Degrees II
Some Recent Developments and New Directions
Keywords:degrees of unsolvability, reducibilities, hierarchies
A transfinite hierarchy of Turing degrees of c.e.\ sets has been used to calibrate the dynamics of families of constructions in computability theory, and yields natural definability results. We review the main results of the area, and discuss splittings of c.e.\ degrees, and finding maximal degrees in upper cones.