A hierarchy for cuppable degrees

作者:Li AS*; Wu GH; Zhang ZY
来源:Illinois Journal of Mathematics, 2000, 44(3): 619-632.

摘要

We say that a computably enumerable (c.e., for short) degree a is cuppable if there is a c.e. degree b not equal 0' such that a boolean OR b = 0'. A c.e. degree a is called low(n)-cuppable, n > 0, if there is a low, c.e. degree 1 such that a boolean OR 1 = 0'. Let LC,, be the set of all low(n)-cuppable c.e. degrees. In this paper, we show that LC1 subset of LC2 subset of or equal to LC3 subset of or equal to (...), so giving a hierarchy for a class of cuppable degrees.