In computability theory two sets of natural numbers are computably isomorphic or recursively isomorphic if there exists a total bijective computable function with . By the Myhill isomorphism theorem, the relation of computable isomorphism coincides with the relation of one-one reduction.
Two numberings and are called computably isomorphic if there exists a computable bijection so that
Computably isomorphic numberings induce the same notion of computability on a set.
- Theorem 7.VI, Hartley Rogers, Jr., Theory of recursive functions and effective computability
- Rogers, Hartley, Jr. (1987), Theory of recursive functions and effective computability (2nd ed.), Cambridge, MA: MIT Press, ISBN 0-262-68052-1, MR 886890.
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