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It is shown that every nonzero r.e. degree contains an r.e. set without the universal splitting property. That is, if 8 is any r.e. nonzero degree, there exist r.e. sets 0 <TB <TA with deg(A) = 8 such that if Ao U Al is an r.e. splitting of A, then Ao * T B. Some generalizations are discussed.

The degrees of r.e. sets without the universal splitting property