Hierarchy of functions | Computability theory | Proof theory

Hardy hierarchy

In computability theory, computational complexity theory and proof theory, the Hardy hierarchy, named after G. H. Hardy, is a hierarchy of sets of numerical functions generated from an ordinal-indexed family of functions hα: N → N (where N is the set of natural numbers, {0, 1, ...}) called Hardy functions. It is related to the fast-growing hierarchy and slow-growing hierarchy. Hardy hierarchy is introduced by Stanley S. Wainer in 1972, but the idea of its definition comes from Hardy's 1904 paper, in which Hardy exhibits a set of reals with cardinality . (Wikipedia).

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Related pages

Large countable ordinal | Fast-growing hierarchy | Grzegorczyk hierarchy | Limit ordinal | G. H. Hardy | Computational complexity theory | Computability theory | Slow-growing hierarchy | Proof theory