Array nonrecursive sets and multiple permitting arguments

We study a class of permitting arguments in which each positive requirement needs multiple permissions to succeed. Three natural examples of such constructions are given. We introduce a class of r. e. sets, the array nonrecursive sets, which consists of precisely those sets which allow enough permission for these constructions be performed. We classify the degrees of array nonrecursive sets and so classify the degrees in which each of these constructions can be performed.