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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 ineffable cardinal ： ウィキペディア英語版 ineffable cardinal In the mathematics of transfinite numbers, an ineffable cardinal is a certain kind of large cardinal number, introduced by . A cardinal number $\backslash kappa$ is called almost ineffable if for every $f:\; \backslash kappa\; \backslash to\; \backslash mathcal(\backslash kappa)$ (where $\backslash mathcal(\backslash kappa)$ is the powerset of $\backslash kappa$) with the property that $f(\backslash delta)$ is a subset of $\backslash delta$ for all ordinals , there is a subset $S$ of $\backslash kappa$ having cardinal $\backslash kappa$ and homogeneous for $f$, in the sense that for any in $S$, $f(\backslash delta\_1)\; =\; f(\backslash delta\_2)\; \backslash cap\; \backslash delta\_1$. A cardinal number $\backslash kappa$ is called ineffable if for every binary-valued function $f\; :\; \backslash mathcal\_(\backslash kappa)\; \backslash to\; \backslash$, there is a stationary subset of $\backslash kappa$ on which $f$ is homogeneous: that is, either $f$ maps all unordered pairs of elements drawn from that subset to zero, or it maps all such unordered pairs to one. More generally, $\backslash kappa$ is called $n$-ineffable (for a positive integer $n$) if for every $f\; :\; \backslash mathcal\_(\backslash kappa)\; \backslash to\; \backslash$ there is a stationary subset of $\backslash kappa$ on which $f$ is $n$-homogeneous (takes the same value for all unordered $n$-tuples drawn from the subset). Thus, it is ineffable if and only if it is 2-ineffable. A totally ineffable cardinal is a cardinal that is $n$-ineffable for every . If $\backslash kappa$ is $(n+1)$-ineffable, then the set of $n$-ineffable cardinals below $\backslash kappa$ is a stationary subset of $\backslash kappa$. Totally ineffable cardinals are of greater consistency strength than subtle cardinals and of lesser consistency strength than remarkable cardinals. A list of large cardinal axioms by consistency strength is available here. ==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「ineffable cardinal」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.