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In set theory, an ordinal number α is an admissible ordinal if Lα is an admissible set (that is, a transitive model of Kripke–Platek set theory); in other words, α is admissible when α is a limit ordinal and Lα⊧Σ0-collection.〔. See in particular (p. 265 ).〕〔.〕 The first two admissible ordinals are ω and for the -th ordinal which is either admissible or a limit of admissibles; an ordinal which is both is called ''recursively inaccessible''.〔. See in particular (p. 560 ).〕 There exists a theory of large ordinals in this manner that is highly parallel to that of (small) large cardinals (one can define recursively Mahlo cardinals, for example).〔.〕 But all these ordinals are still countable. Therefore, admissible ordinals seem to be the recursive analogue of regular cardinal numbers. Notice that α is an admissible ordinal if and only if α is a limit ordinal and there does not exist a γ<α for which there is a Σ1(Lα) mapping from γ onto α. If M is a standard model of KP, then the set of ordinals in M is an admissible ordinal. ==See also== *Large countable ordinals *Inaccessible cardinal *Constructible universe 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「Admissible ordinal」の詳細全文を読む スポンサード リンク
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