The cupping theorem in R/M
Sui Yuefei, Zhang Zaiyue · Journal of Symbolic Logic · 1999
Abstract It will be proved that the Shoenfield cupping conjecture holds in R/M, the quotient of the recursively enumerable degrees modulo the cappable r.e. degrees. Namely, for any [a], [b] ∈ R/M such that [0] ≺ [b] ≺ [a] there exists [c] ∈ R/M such that [c] ≺ [a] and [a] = [b] ∨ [c].