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In [[computability theory (computer science)|computability theory]] two sets <math>A;B \subseteq \N</math> of [[natural number]]s are '''computably isomorphic''' or '''recursively isomorphic''' if there exists a [[Total function|total]] [[bijective]] [[computable function]] <math>f \colon \N \to \N</math> with <math>f(A) = B</math>.
 
Two [[numbering (computability theory)|numbering]]s <math>\nu</math> and <math>\mu</math> are called '''computably isomorphic''' if there exists a computable bijection <math>f</math> so that <math>\nu = \mu \circ f</math>
 
Computably isomorphic numberings induce the same notion of computability on a set.
 
== References ==
*{{citation
| last = Rogers | first = Hartley, Jr. | author-link = Hartley Rogers, Jr.
| edition = 2nd
| isbn = 0-262-68052-1
| location = Cambridge, MA
| mr = 886890
| publisher = MIT Press
| title = Theory of recursive functions and effective computability
| year = 1987}}.  
 
 
{{DEFAULTSORT:Computable Isomorphism}}
[[Category:Theory of computation]]
[[Category:Computability theory]]
 
 
{{comp-sci-theory-stub}}
{{mathlogic-stub}}

Revision as of 22:27, 21 December 2013

In computability theory two sets A;B of natural numbers are computably isomorphic or recursively isomorphic if there exists a total bijective computable function f: with f(A)=B.

Two numberings ν and μ are called computably isomorphic if there exists a computable bijection f so that ν=μf

Computably isomorphic numberings induce the same notion of computability on a set.

References

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