1. Institute of Software, Chinese Academy of Sciences, Beijing 100080, China;School of Information Sciences, Beijing Normal University, Beijing 100871,China 2. Institute of Software, Chinese Academy of Sciences, Beijing 100080, China
Abstract:
A computably enumerable (c.e., for short) degree a is called plus cupping, if every c.e. degree x with 0 is cuppable. Let PC be the set of all plus cupping degrees. In the present paper, we show that PC is not closed under the join operation v by constructing two plus cupping degrees which join to a high degree. So by the Harrington’s noncupping theorem, PC is not an ideal of ε.
