Turing degree
Many hypercomputation proposals amount to alternative ways to read an oracle or advice function embedded into an otherwise classical machine. Others allow access to some higher level of the arithmetic hierarchy. For example, supertasking Turing machines, under the usual assumptions, would be able to compute any predicate in the truth-table degree containing formula_3 or formula_4. Limiting-recursion, by contrast, can compute any predicate or function in the corresponding Turing degree, which is known to be formula_5. Gold further showed that limiting partial recursion would allow the computation of precisely the formula_6 predicates.