Low upper bounds in the Turing degrees revisited


G. Barmpalias and Andre Nies

Summary


We give an alternative proof of a result of Ku\v{c}era and Slaman on low bounds of ideals in the $\Delta^0_2$ Turing degrees. This is a characterization of the ideals in the $\Delta^0_2$ degrees which have a low upper bound. It follows that there is a low upper bound for the ideal of the K-trivial degrees. Our proof is direct, in the sense that it does not use universal classes of PA degrees.