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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 Wadge hierarchy ： ウィキペディア英語版 Wadge hierarchy In descriptive set theory, Wadge degrees are levels of complexity for sets of reals. Sets are compared by continuous reductions. The Wadge hierarchy is the structure of Wadge degrees. == Wadge degrees == Suppose $A$ and $B$ are subsets of Baire space ωω. $A$ is Wadge reducible to $B$ or $A$ ≤W $B$ if there is a continuous function $f$ on ωω with $A\; =\; f^()$. The Wadge order is the preorder or quasiorder on the subsets of Baire space. Equivalence classes of sets under this preorder are called Wadge degrees, the degree of a set $A$ is denoted by ()W. The set of Wadge degrees ordered by the Wadge order is called the Wadge hierarchy. Properties of Wadge degrees include their consistency with measures of complexity stated in terms of definability. For example, if $A$ ≤W $B$ and $B$ is a countable intersection of open sets, then so is $A$. The same works for all levels of the Borel hierarchy and the difference hierarchy. The Wadge hierarchy plays an important role in models of the axiom of determinacy. Further interest in Wadge degrees comes from computer science, where some papers have suggested Wadge degrees are relevant to algorithmic complexity. 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「Wadge hierarchy」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.