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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>.
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| 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>
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| Computably isomorphic numberings induce the same notion of computability on a set.
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| == References ==
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| *{{citation
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| | last = Rogers | first = Hartley, Jr. | author-link = Hartley Rogers, Jr.
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| | edition = 2nd
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| | isbn = 0-262-68052-1
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| | location = Cambridge, MA
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| | mr = 886890
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| | publisher = MIT Press
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| | title = Theory of recursive functions and effective computability
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| | year = 1987}}.
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| {{DEFAULTSORT:Computable Isomorphism}}
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| [[Category:Theory of computation]]
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| [[Category:Computability theory]]
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| {{comp-sci-theory-stub}}
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| {{mathlogic-stub}}
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Latest revision as of 20:17, 19 November 2014
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