Computable isomorphism

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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,[1] 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.


  1. ^ Theorem 7.VI, Hartley Rogers, Jr., Theory of recursive functions and effective computability