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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 Index set (recursion theory) ： ウィキペディア英語版 Index set (recursion theory) In the field of recursion theory, index sets describe classes of partial recursive functions, specifically they give all indices of functions in that class according to a fixed enumeration of partial recursive functions (a Gödel numbering). ==Definition== Fix an enumeration of all partial recursive functions, or equivalently of recursively enumerable sets whereby the ''e''th such set is $W\_$ and the ''e''th such function (whose domain is $W\_$) is $\backslash phi\_$. Let $\backslash mathcal$ be a class of partial recursive functions. If $A\; =\; \backslash \; \backslash \}$ then $A$ is the index set of $\backslash mathcal$. In general $A$ is an index set if for every $x,y\; \backslash in\; \backslash mathbb$ with $\backslash phi\_x\; \backslash simeq\; \backslash phi\_y$ (i.e. they index the same function), we have $x\; \backslash in\; A\; \backslash leftrightarrow\; y\; \backslash in\; A$. Intuitively, these are the sets of natural numbers that we describe only with reference to the functions they index. 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「Index set (recursion theory)」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.