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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 definable set ： ウィキペディア英語版 definable set In mathematical logic, a definable set is an ''n''-ary relation on the domain of a structure whose elements are precisely those elements satisfying some formula in the language of that structure. A set can be defined with or without parameters, which are elements of the domain that can be referenced in the formula defining the relation. == Definition == Let $\backslash mathcal$ be a first-order language, $\backslash mathcal$ an $\backslash mathcal$-structure with domain $M$, $X$ a fixed subset of $M$, and $m$ a natural number. Then: * A set $A\backslash subseteq\; M^m$ is ''definable in $\backslash mathcal$ with parameters from $X$'' if and only if there exists a formula $\backslash varphi()$ and elements $b\_1,\backslash ldots,b\_n\backslash in\; X$ such that for all $a\_1,\backslash ldots,a\_m\backslash in\; M$, :$(a\_1,\backslash ldots,a\_m)\backslash in\; A$ if and only if $\backslash mathcal\backslash models\backslash varphi()$ :The bracket notation here indicates the semantic evaluation of the free variables in the formula. * A set ''$A$ is definable in $\backslash mathcal$ without parameters'' if it is definable in $\backslash mathcal$ with parameters from the empty set (that is, with no parameters in the defining formula). * A function is definable in $\backslash mathcal$ (with parameters) if its graph is definable (with those parameters) in $\backslash mathcal$. * An element $a$ is definable in $\backslash mathcal$ (with parameters) if the singleton set $\backslash$ is definable in $\backslash mathcal$ (with those parameters). 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「definable set」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.