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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 homogeneous tree ： ウィキペディア英語版 homogeneous tree In descriptive set theory, a tree over a product set $Y\backslash times\; Z$ is said to be homogeneous if there is a system of measures $\backslash langle\backslash mu\_s\backslash mid\; s\backslash in$ . * The measures are in some sense compatible under restriction of sequences: if $s\_1\backslash subseteq\; s\_2$, then $\backslash mu\_(X)=1\backslash iff\backslash mu\_(\backslash )=1$. * If $x$ is in the projection of $T$, the ultrapower by $\backslash langle\backslash mu\_\backslash mid\; n\backslash in\backslash omega\backslash rangle$ is wellfounded. An equivalent definition is produced when the final condition is replaced with the following: * There are $\backslash langle\backslash mu\_s\backslash mid\; s\backslash in^\backslash omega\; Z$ such that $\backslash forall\; n\backslash in\backslash omega\backslash ,f\backslash upharpoonright\; n\backslash in\; X\_n$. This condition can be thought of as a sort of countable completeness condition on the system of measures. $T$ is said to be $\backslash kappa$-homogeneous if each $\backslash mu\_s$ is $\backslash kappa$-complete. Homogeneous trees are involved in Martin and Steel's proof of projective determinacy. ==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「homogeneous tree」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.