Computable isomorphism
Appearance
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In computability theory two sets of natural numbers are computably isomorphic or recursively isomorphic if there exists a total computable and bijective function such that the image of restricted to equals , i.e. .
Further, 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.
Theorems
[edit]By the Myhill isomorphism theorem, the relation of computable isomorphism coincides with the relation of mutual one-one reducibility.[1]
References
[edit]- ^ 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 0886890.