Editing Computable function (section)

===Higher recursion theory===

[[Hyperarithmetical theory]] studies those sets that can be computed from a [[computable ordinal]] number of iterates of the [[Turing jump]] of the empty set. This is equivalent to sets defined by both a universal and existential formula in the language of second order arithmetic and to some models of [[Hypercomputation]]. Even more general recursion theories have been studied, such as '''E-recursion theory''' in which any set can be used as an argument to an E-recursive function.