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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 Laver property ： ウィキペディア英語版 Laver property In mathematical set theory, the Laver property holds between two models if they are not "too dissimilar", in the following sense. For $M$ and $N$ transitive models of set theory, $N$ is said to have the Laver property over $M$ if and only if for every function $g\backslash in\; M$ mapping $\backslash omega$ to $\backslash omega\backslash setminus\backslash$ such that $g$ diverges to infinity, and every function $f\backslash in\; N$ mapping $\backslash omega$ to $\backslash omega$ and every function $h\backslash in\; M$ which bounds $f$, there is a tree $T\backslash in\; M$ such that each branch of $T$ is bounded by $h$ and for every $n$ the $n^\backslash text$ level of $T$ has cardinality at most $g(n)$ and $f$ is a branch of $T$.〔Shelah, S., Consistently there is no non-trivial ccc forcing notion with the Sacks or Laver property, Combinatorica, vol. 2, pp. 309 -- 319, (2001)〕 A forcing notion is said to have the Laver property if and only if the forcing extension has the Laver property over the ground model. Examples include Laver forcing. The concept is named after Richard Laver. Shelah proved that when proper forcings with the Laver property are iterated using countable supports, the resulting forcing notion will have the Laver property as well.〔Shelah, S., Proper and Improper Forcing, Springer (1992)〕〔C. Schlindwein, Understanding preservation theorems: Chapter VI of Proper and Improper Forcing, I. Archive for Mathematical Logic, vol. 53, 171–202, Springer, 2014〕 The conjunction of the Laver property and the $\{\}^\backslash omega\backslash omega$-bounding property is equivalent to the Sacks property. ==References== 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「Laver property」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.