Computable nondeterministic functions

Functions computed on nondeterministic machines consist of two parts. The halting part which consists of outputs of halting computations, is, as expected, recursively enumerable. The divergence part, which consists of inputs for which diverging computations are possible, can however be any set in Σ11. Such highly noncomputable sets arise if one admits the "finite delay property". This implies that either we make a significant modification to our notion of "computable" as applied to nondeterministic machine models, or else that we ban the finite delay property for nondeterministic models.