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P.R.-Regulated Systems of Notation and the Subrecursive Hierarchy Equivalence Property

1977
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Transactions of the American Mathematical Society
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We can attempt to extend the Grzegorczyk Hierarchy transfinitely by defining a sequence of functions indexed by the elements of a system of notation S, using either iteration (majorization) or enumeration techniques to define the functions. (The hierarchy is then the sequence of classes of functions elementary in the functions of the sequence of functions.) In this paper we consider two sequences {Fs)s£i and {G,}jeS defined by iteration and a sequence (£,},eS defined by enumeration; the

doi:10.2307/1997995
fatcat:jxjl7zx7yvf2de4jkhqoefzynm