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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 Π01 class ： ウィキペディア英語版 Π01 class In computability theory, a Π01 class is a subset of 2ω of a certain form. These classes are of interest as a technical tool within recursion theory and effective descriptive set theory. They are also used in the application of recursion theory to other branches of mathematics (Cenzer 1999, p. 39). == Definition == The set 2< ω consists of all finite sequences of 0s and 1s, while the set 2ω consists of all infinite sequences of 0s and 1s (that is, functions from } to the set }). A tree on 2< ω is a subset of 2<ω that is closed under taking initial segments. An element ''f'' of 2ω is a path through a tree ''T'' on 2< ω if every finite initial segment of ''f'' is in ''T''. A (lightface) Π01 class is a subset ''C'' of 2ω for which there is a computable tree ''T'' such that ''C'' consists of exactly the paths through ''T''. A boldface Π01 class is a subset ''D'' of 2ω for which there is an oracle ''f'' in 2ω and a subtree tree ''T'' of 2< ω from computable from ''f'' such that ''D'' is the set of paths through ''T''. 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「Π01 class」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.