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 any n, 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.

中文翻译：

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可计算的度数中的拔罐和跳跃类

我们表明存在可拔罐的 ce 度数，其所有拔罐伙伴都很高。特别是，并非所有可杯测度数都是${\operatorname {\mathrm {low}}}_3$-杯子，或者确实${\operatorname {\mathrm {low}}}_n$任何人都可以喝n，驳斥了李某的猜想。另一方面，我们表明一个人不能将高位提升到超高位。我们还表明，${\operatorname {\mathrm {low}}}_2$-cuppable degree 与 array 可计算可杯化度数相吻合，从而全面了解后一类。