Complementing cappable degrees in the difference hierarchy Original Research Article

We prove that for any computably enumerable (c.e.) degree View the MathML source, if it is cappable in the computably enumerable degrees, then there is a d.c.e. degree View the MathML source such that View the MathML source and View the MathML source. Consequently, a computably enumerable degree is cappable if and only if it can be complemented by a nonzero d.c.e. degree. This gives a new characterization of the cappable degrees.