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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 Complete numbering ： ウィキペディア英語版 Complete numbering In computability theory complete numberings are generalizations of Gödel numbering first introduced by A.I. Mal'tsev in 1963. They are studied because several important results like the Kleene's recursion theorem and Rice's theorem, which were originally proven for the Gödel-numbered set of computable functions, still hold for arbitrary sets with complete numberings. == Definition == A numbering $\backslash nu$ of a set $A$ is called complete (with respect to an element $a\; \backslash in\; A$) if for every partial computable function $f$ there exists a total computable function $h$ so that :$\backslash nu\; \backslash circ\; h(i)\; =$ \left\\ i \in \mathrm(f), \\ a &\mbox. \end \right. The numbering $\backslash nu$ is called precomplete if :$\backslash nu\; \backslash circ\; f(i)\; =\; \backslash nu\; \backslash circ\; h(i)\; \backslash qquad\; i\; \backslash in\; \backslash mathrm(f).\backslash ,$ == Examples == * any numbering of a singleton set is complete * the identity function on the natural numbers is ''not'' complete * a Gödel numbering is precomplete 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「Complete numbering」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.