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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 Recursive ordinal ： ウィキペディア英語版 Recursive ordinal In mathematics, specifically set theory, an ordinal $\backslash alpha$ is said to be recursive if there is a recursive well-ordering of a subset of the natural numbers having the order type $\backslash alpha$. It is trivial to check that $\backslash omega$ is recursive, the successor of a recursive ordinal is recursive, and the set of all recursive ordinals is closed downwards. The supremum of all recursive ordinals is called the Church-Kleene ordinal and denoted by $\backslash omega^\_1$. Indeed, an ordinal is recursive if and only if it is smaller than $\backslash omega^\_1$. Since there are only countably many recursive relations, there are also only countably many recursive ordinals. Thus, $\backslash omega^\_1$ is countable. The recursive ordinals are exactly the ordinals that have an ordinal notation in Kleene's $\backslash mathcal$. ==See also== *Arithmetical hierarchy *Large countable ordinals *Ordinal notation 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「Recursive ordinal」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.