Turing reduction
It therefore suffices to show that if limit computability is preserved by Turing reduction, as this will show that all sets computable from formula_9 are limit computable. Fix sets formula_25 which are identified with their characteristic functions and a computable function formula_26 with limit formula_27. Suppose that formula_28 for some Turing reduction formula_29 and define a computable function formula_30 as follows