翻訳と辞書 Words near each other ・ Uniformed Services Benefit Association ・ Uniformed Services Employment and Reemployment Rights Act ・ Uniformed Services Former Spouses' Protection Act ・ Uniformed services of the United States ・ Uniformed Services University of the Health Sciences ・ Uniformitarianism ・ Uniformity ・ Uniformity and jurisdiction in U.S. federal court tax decisions ・ Uniformity of content ・ Uniformity of motive ・ Uniformity policy ・ Uniformity tape ・ Uniformizable space ・ Uniformization ・ Uniformization (probability theory) ・ Uniformization (set theory) ・ Uniformization theorem ・ Uniformly bounded representation ・ Uniformly Cauchy sequence ・ Uniformly connected space ・ Uniformly convex space ・ Uniformly distributed measure ・ Uniformly hyperfinite algebra ・ Uniformly most powerful test ・ Uniformly smooth space ・ Uniformology ・ Uniforms and insignia of the Kriegsmarine ・ Uniforms and insignia of the Schutzstaffel ・ Uniforms and insignia of the Sturmabteilung ・ Uniforms of Iraqi Armed Forces Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Uniformization (set theory) ： ウィキペディア英語版 Uniformization (set theory) In set theory, the axiom of uniformization, a weak form of the axiom of choice, states that if $R$ is a subset of $X\backslash times\; Y$, where $X$ and $Y$ are Polish spaces, then there is a subset $f$ of $R$ that is a partial function from $X$ to $Y$, and whose domain (in the sense of the set of all $x$ such that $f(x)$ exists) equals : $\backslash \backslash ,$ Such a function is called a uniformizing function for $R$, or a uniformization of $R$. To see the relationship with the axiom of choice, observe that $R$ can be thought of as associating, to each element of $X$, a subset of $Y$. A uniformization of $R$ then picks exactly one element from each such subset, whenever the subset is nonempty. Thus, allowing arbitrary sets ''X'' and ''Y'' (rather than just Polish spaces) would make the axiom of uniformization equivalent to AC. A pointclass $\backslash boldsymbol$ is said to have the uniformization property if every relation $R$ in $\backslash boldsymbol$ can be uniformized by a partial function in $\backslash boldsymbol$. The uniformization property is implied by the scale property, at least for adequate pointclasses of a certain form. It follows from ZFC alone that $\backslash boldsymbol^1\_1$ and $\backslash boldsymbol^1\_2$ have the uniformization property. It follows from the existence of sufficient large cardinals that *$\backslash boldsymbol^1\_$ and $\backslash boldsymbol^1\_$ have the uniformization property for every natural number $n$. *Therefore, the collection of projective sets has the uniformization property. *Every relation in L(R) can be uniformized, but ''not necessarily'' by a function in L(R). In fact, L(R) does not have the uniformization property (equivalently, L(R) does not satisfy the axiom of uniformization). * *(Note: it's trivial that every relation in L(R) can be uniformized ''in V'', assuming V satisfies AC. The point is that every such relation can be uniformized in some transitive inner model of V in which AD holds.) == 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「Uniformization (set theory)」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.