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In computability theory, computational complexity theory and proof theory, the Hardy hierarchy, named after G. H. Hardy, is an ordinal-indexed family of functions ''h''α: N → N (where N is the set of natural numbers, ). It is related to the fast-growing hierarchy and slow-growing hierarchy. The hierarchy was first described in Hardy's 1904 paper, "A theorem concerning the infinite cardinal numbers". == Definition == Let μ be a large countable ordinal such that a fundamental sequence is assigned to every limit ordinal less than μ. The Hardy hierarchy of functions ''h''α: N → N, for ''α'' < ''μ'', is then defined as follows: * * * if α is a limit ordinal. Here α() denotes the ''n''th element of the fundamental sequence assigned to the limit ordinal ''α''. A standardized choice of fundamental sequence for all ''α'' ≤ ''ε''0 is described in the article on the fast-growing hierarchy. Caicedo (2007) defines a modified Hardy hierarchy of functions by using the standard fundamental sequences, but with α() (instead of α()) in the third line of the above definition. 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「Hardy hierarchy」の詳細全文を読む スポンサード リンク
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