In computability theory of natural numbers are computably isomorphic or recursively isomorphic if there exists a total computable and bijective.

Further, two numberings (of the same set of objects) are called computably isomorphic. Computably isomorphic numberings induce the same notion of computability on a set.

Theorems

By the Myhill isomorphism theorem, the relation of computably isomorphic coincides with the relation of mutual one-one reducibility.

References

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