Finite cupping sets

We show that there exists a single minimal (Turing) degree b < 0 s.t. for all c.e. degrees 0 < a < 0 , 0 = a b. Since b is minimal this means that b complements all c.e. degrees 0 < a < 0 . Since every n-c.e. degree bounds a (non-zero) c.e. degree, b complements every n-c.e. degree 0 < a < 0 .

• Type: Journal
• Year: 2004
• Where: AML
• Authors: Andrew Lewis
• Keywords: AML 2004, Non-zero, Turing