Low basis theorem

The low basis theorem in computability theory states that every nonempty Π 1 0 class in 2 ω (see arithmetical hierarchy) contains a set of low degree (Soare 1987:109). It was first proved by Carl Jockusch and Robert I. Soare in 1972 (Nies 2009:57). Cenzer (1993:53) describes it as "perhaps the most cited result in the theory of Π 1 0 classes". The proof uses the method of forcing with Π 1 0 classes (Cooper 2004:330).