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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 Proper forcing axiom ： ウィキペディア英語版 Proper forcing axiom In the mathematical field of set theory, the proper forcing axiom (''PFA'') is a significant strengthening of Martin's axiom, where forcings with the countable chain condition (ccc) are replaced by proper forcings. == Statement == A forcing or partially ordered set P is proper if for all regular uncountable cardinals $\backslash lambda$, forcing with P preserves stationary subsets of $()^\backslash omega$. The proper forcing axiom asserts that if P is proper and Dα is a dense subset of P for each α<ω1, then there is a filter G $\backslash subseteq$ P such that Dα ∩ G is nonempty for all α<ω1. The class of proper forcings, to which PFA can be applied, is rather large. For example, standard arguments show that if P is ccc or ω-closed, then P is proper. If P is a countable support iteration of proper forcings, then P is proper. Crucially, all proper forcings preserve $\backslash aleph\_1$. 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「Proper forcing axiom」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.