Maximal Pairs of Computably Enumerable Sets in the Computably Lipschitz Degrees

@article{AmbosSpies2012MaximalPO,
  title={Maximal Pairs of Computably Enumerable Sets in the Computably Lipschitz Degrees},
  author={Klaus Ambos-Spies and Decheng Ding and Yun Fan and Wolfgang Merkle},
  journal={Theory of Computing Systems},
  year={2012},
  volume={52},
  pages={2-27}
}
A set A is computably Lipschitz or cl-reducible, for short, to a set B if A is Turing reducible to B by an oracle Turing machine with use function ϕ such that ϕ is bounded by the identity function up to an additive constant, i.e., ϕ(n)≤n+O(1). In this paper we study maximal pairs of computably enumerable (c.e.) cl-degrees or maximal pairs, for short, i.e., pairs of c.e. cl-degrees such that there is no c.e. cl-degree that is above both cl-degrees in this pair. Our main results are as follows… CONTINUE READING