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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 Condensation lemma ： ウィキペディア英語版 Condensation lemma In set theory, a branch of mathematics, the condensation lemma is a result about sets in the constructible universe. It states that if ''X'' is a transitive set and is an elementary submodel of some level of the constructible hierarchy Lα, that is, $(X,\backslash in)\backslash prec\; (L\_\backslash alpha,\backslash in)$, then in fact there is some ordinal $\backslash beta\backslash leq\backslash alpha$ such that $X=L\_\backslash beta$. More can be said: If ''X'' is not transitive, then its transitive collapse is equal to some $L\_\backslash beta$, and the hypothesis of elementarity can be weakened to elementarity only for formulas which are $\backslash Sigma\_1$ in the Lévy hierarchy. Also, the assumption that ''X'' be transitive automatically holds when $\backslash alpha=\backslash omega\_1$. The lemma was formulated and proved by Kurt Gödel in his proof that the axiom of constructibility implies GCH. == References == * (theorem II.5.2 and lemma II.5.10) 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「Condensation 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.