A single minimal complement for the c.e. degrees

Abstract

We show that there exists a minimal (Turing) degree b > 0 ′ b>0’ such that for all non-zero c.e. degrees a a , 0 ′ = a ∨ b 0’=a\vee b . Since b b is minimal this means that b b complements all c.e. degrees other than 0 0 and 0 ′ 0’ . Since every n n -c.e. degree bounds a non-zero c.e. degree, b b complements every n n -c.e. degree other than 0 0 and 0 ′ 0’ .