The cupping theorem in r/m

Journal of Symbolic Logic 64 (2):643-650 (1999)
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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] $\prec$ [b] $\prec$ [a] there exists [c] ∈ R/M such that [c] $\prec$ [a] and [a] = [b] ∨ [c]



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