Computable isomorphism
In computability theory two sets formula_1 of natural numbers are computably isomorphic or recursively isomorphic if there exists a total bijective computable function formula_2 with formula_3. By the Myhill isomorphism theorem, the relation of computable isomorphism coincides with the relation of mutual one-one reducibility. Two numberings formula_4 and formula_5 are called computably isomorphic if there exists a computable bijection formula_6 so that formula_7 Computably isomorphic numberings induce the same notion of computability on a set.