摘要
A computably enumerable (c.e.,for short)degree a is called plus cupping,if every c.e. degree x with 0<x≤a 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 ∨ by constructing two plus cupping degrees which join to a high degree. So by the Harringtons noncupping theorem,PC is not an ideal of ε.
A computably enumerable (c.e.,for short)degree a is called plus cupping,if every c.e. degree x with 0<x≤a 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 ∨ by constructing two plus cupping degrees which join to a high degree. So by the Harringtons noncupping theorem,PC is not an ideal of ε.
