# A single minimal complement for the c.e. degrees

@inproceedings{LewisPye2007ASM, title={A single minimal complement for the c.e. degrees}, author={Andrew Lewis-Pye}, year={2007} }

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