Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
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Cholak, Groszek and Slaman proved in [1] that there is a nonzero computably enumerable (c.e.) degree cupping every low c.e. degree to a low c.e. degree. In the same paper, they pointed out that every nonzero c.e. degree can cup a low2c.e. degree to a nonlow2degree. In [2], Jockusch, Li and Yang improved the latter result by showing that every nonzero c.e. degree cis cuppable to a high c.e. degree by a low2c.e. degree b. It is natural to ask in which subclass of low2c.e. degrees bin [2] can be located. Wu proved [6] that bcan be cappable. We prove in this paper that bin Jockusch, Li and Yang's result can be noncuppable, improving both Jockusch, Li and Yang, and Wu's results.