Uniform enumeration operations

Journal of Symbolic Logic 40 (3):401-409 (1975)
Sacks [2] has asked whether there exists a uniform solution to Post's problem, i.e. an enumeration operation W such that $\mathbf{d} for every degree d. It is shown here that if such an operation W exists it cannot itself in a particular technical sense be uniform. In fact, the jump operation is characterized amongst such uniform enumeration operations by the condition: $\mathbf{d} for all d. In addition, it is proved that the only other uniform enumeration operations such that d ≤ W (d) for all d are those which equal the identity operation above some fixed degrees
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