CUPPING AND JUMP CLASSES IN THE COMPUTABLY ENUMERABLE DEGREES
Noam Greenberg, Keng Meng Ng, Guohua Wu · Journal of Symbolic Logic · 2020
Abstract We show that there is a cuppable c.e. degree, all of whose cupping partners are high. In particular, not all cuppable degrees are ${\operatorname {\mathrm {low}}}_3$ -cuppable, or indeed ${\operatorname {\mathrm {low}}}_n$ cuppable for anyn, refuting a conjecture by Li. On the other hand, we show that one cannot improve highness to superhighness. We also show that the ${\operatorname {\mathrm {low}}}_2$ -cuppable degrees coincide with the array computable-cuppable degrees, giving a full understanding of the latter class.