Cuppability of simple and hypersimple sets (Q2469430)

The paper is devoted to cuppable degrees, where an incomplete degree is cuppable iff it can be joined by an incomplete degreee to a complete degree. For sets fulfilling some properties one can ask whether they are cuppable with respect to a certain type of reducibilities. Some results of this sort are known. In the paper under review all the remaining cases for the standard notions of simplicity and all the main strong reducibilities are settled, in particular the case of truth-table reductions, conjunctive, disjunctive, bounded truth-table reducibilities, parity reduction and \(Q\)-reducibility.