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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 Fodor's lemma ： ウィキペディア英語版 Fodor's lemma In mathematics, particularly in set theory, Fodor's lemma states the following: If $\backslash kappa$ is a regular, uncountable cardinal, $S$ is a stationary subset of $\backslash kappa$, and $f:S\backslash rightarrow\backslash kappa$ is regressive (that is, for any $\backslash alpha\backslash in\; S$, $\backslash alpha\backslash neq\; 0$) then there is some $\backslash gamma$ and some stationary $S\_0\backslash subseteq\; S$ such that $f(\backslash alpha)=\backslash gamma$ for any $\backslash alpha\backslash in\; S\_0$. In modern parlance, the nonstationary ideal is ''normal''. ==Proof== We can assume that $0\backslash notin\; S$ (by removing 0, if necessary). If Fodor's lemma is false, for every there is some club set $C\_\backslash alpha$ such that $C\_\backslash alpha\backslash cap\; f^(\backslash alpha)=\backslash emptyset$. Let $C=\backslash Delta\_\; C\_\backslash alpha$. The club sets are closed under diagonal intersection, so $C$ is also club and therefore there is some $\backslash alpha\backslash in\; S\backslash cap\; C$. Then $\backslash alpha\backslash in\; C\_\backslash beta$ for each , and so there can be no such that $\backslash alpha\backslash in\; f^(\backslash beta)$, so $f(\backslash alpha)\backslash geq\backslash alpha$, a contradiction. The lemma was first proved by the Hungarian set theorist, Géza Fodor in 1956. It is sometimes also called "The Pressing Down Lemma". Fodor's lemma also holds for Thomas Jech's notion of stationary sets as well as for the general notion of stationary set. 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「Fodor's lemma」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.