The upper semilattice of degrees = 0' is complemented

Let denote the set of degrees = 0'. A degree a= 0' is said to be complementedin if there exists a degree b= 0' such that b? a= 0' and bn a= 0. R.W. Robinson (cf. [11]) showed that every degree a= 0' satisfying a? = 0? is complemented in and the author [8] showed that every degree a= 0' satisfying a' = 0? is complemented in . Also, in [2], R. L. Epstein showed that every r.e. degree is complemented in . In this paper we will show that in fact every degree = 0' is complemented in . We will further show that the same is true in the upper semilattice of degrees = c, where cis any complete degree. This is in contrast to the situation in the upper semilattice of r.e. degrees in which, as Lachlan [6] has shown, no degree other than 0and 0' is complemented.