关键词: turing degrees, recursive enumerability, distributivity

Abstract: It will be proved that given any noncappable r.e. degree a there are r.e.degrees a ₀ and a ₁ such that a ₀,a ₁<=a and [a ₀∪a ₁] is not local distributive,i.e.,there is an r.e.degree c such that [c][a ₀∪a ₁] and for any [u _i][a _i] and i=0,1,[c]≠[u ₀]∨[u ₁] where R/M is the quotient of the recursively enumerable degrees modulo the cappable degrees. Therefore, R/M is not distributive. 

Key words: turing degrees, recursive enumerability, distributivity