Prompt permissions

This chapter explores prompt versions of all levels in the hierarchy. This generalises the already familiar notion of prompt permitting, which is the prompt version of simple permitting. Prompt array noncomputable permission, for example, allows one to construct a pair of separating classes whose elements form minimal pairs (Theorem 8.22). Meanwhile, traditional (non-prompt) array noncomputable permission only gives Turing incomparability. There are at least two ways to get such an embedding: either by quickly getting the precise number of permissions required; or by getting many permissions (cofinitely many), in which case one can wait for the permissions and do not need them promptly.