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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 prewellordering ： ウィキペディア英語版 prewellordering In set theory, a prewellordering is a binary relation $\backslash le$ that is transitive, total, and wellfounded (more precisely, the relation $x\backslash le\; y\backslash land\; y\backslash nleq\; x$ is wellfounded). In other words, if $\backslash leq$ is a prewellordering on a set $X$, and if we define $\backslash sim$ by :$x\backslash sim\; y\backslash iff\; x\backslash leq\; y\; \backslash land\; y\backslash leq\; x$ then $\backslash sim$ is an equivalence relation on $X$, and $\backslash leq$ induces a wellordering on the quotient $X/\backslash sim$. The order-type of this induced wellordering is an ordinal, referred to as the length of the prewellordering. A norm on a set $X$ is a map from $X$ into the ordinals. Every norm induces a prewellordering; if $\backslash phi:X\backslash to\; Ord$ is a norm, the associated prewellordering is given by :$x\backslash leq\; y\backslash iff\backslash phi(x)\backslash leq\backslash phi(y)$ Conversely, every prewellordering is induced by a unique regular norm (a norm $\backslash phi:X\backslash to\; Ord$ is regular if, for any $x\backslash in\; X$ and any , there is $y\backslash in\; X$ such that $\backslash phi(y)=\backslash alpha$). == Prewellordering property == If $\backslash boldsymbol$ is a pointclass of subsets of some collection $\backslash mathcal$ of Polish spaces, $\backslash mathcal$ closed under Cartesian product, and if $\backslash leq$ is a prewellordering of some subset $P$ of some element $X$ of $\backslash mathcal$, then $\backslash leq$ is said to be a $\backslash boldsymbol$-prewellordering of $P$ if the relations *\, and $\backslash leq^$ * are elements of $\backslash boldsymbol$, where for $x,y\backslash in\; X$, # *y\iff x\in P\land(P\lor\ ) # $x\backslash leq^$ * y\iff x\in P\land(P\lor x\leq y ) $\backslash boldsymbol$ is said to have the prewellordering property if every set in $\backslash boldsymbol$ admits a $\backslash boldsymbol$-prewellordering. The prewellordering property is related to the stronger scale property; in practice, many pointclasses having the prewellordering property also have the scale property, which allows drawing stronger conclusions. 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「prewellordering」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.