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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Myhill isomorphism theorem ： ウィキペディア英語版 Myhill isomorphism theorem In computability theory the Myhill isomorphism theorem, named after John Myhill, provides a characterization for two numberings to induce the same notion of computability on a set. == Myhill isomorphism theorem == Sets ''A'' and ''B'' of natural numbers are said to be recursively isomorphic if there is a total computable bijection ''f'' from the set of natural numbers to itself such that ''f''(''A'') = ''B''. A set ''A'' of natural numbers is said to be one-one reducible to a set ''B'' if there is a total computable injection ''f'' on the natural numbers such that $f(A)\; \backslash subseteq\; B$ and $f(\backslash mathbb\; \backslash setminus\; A)\; \backslash subseteq\; \backslash mathbb\; \backslash setminus\; B$. Myhill's isomorphism theorem states that two sets ''A'' and ''B'' of natural numbers are recursively isomorphic if and only if ''A'' is one-reducible to ''B'' and ''B'' is one-reducible to ''A''. The theorem is proved by an effective version of the argument used for the Schroeder–Bernstein theorem. A corollary of Myhill's theorem is that two total numberings are one-equivalent if and only if they are computably isomorphic. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Myhill isomorphism theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.