In 1990, Downey, Jockusch and Stob introduced array non-computable sets which capture certain multiple permitting arguments. They completely characterize the simplicity notions which are compatible with array noncomputability. Here we generalize this question and ask for which simplicity properties P there exist c.e. wtt-degrees that contain both sets with property P and array noncomputable sets. By showing that there exists an r-maximal set which is wtt-equivalent to an array noncomputable set we obtain a complete answer to this question for the standard simplicity notions.
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