Plain Bases for Classes of Primitive Recursive Functions

Mathematical Logic Quarterly 48 (1):93-104 (2002)
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Abstract

A basis for a set C of functions on natural numbers is a set F of functions such that C is the closure with respect to substitution of the projection functions and the functions in F. This paper introduces three new bases, comprehending only common functions, for the Grzegorczyk classes ℰ_n with n ≥ 3. Such results are then applied in order to show that ℰ_{n+1} = K_n for n ≥ 2, where {K_n}n∈ℕ is the Axt hierarchy.

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10.1002/1521-3870(200201)48:1

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Citations of this work

New substitution bases for complexity classes.Stefano Mazzanti - 2020 - Mathematical Logic Quarterly 66 (1):37-50.

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References found in this work

Iteration of Primitive Recursion.Paul Axt - 1965 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 11 (3):253-255.
Hierarchies of Primitive Recursive Functions.Charles Parsons - 1968 - Mathematical Logic Quarterly 14 (21-24):357-376.
Über die eliminierbarkeit Von definitionsschemata in der theorie der rekursiven funktionen.Dieter Rödding - 1964 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 10 (18):315-330.
Iteration of Primitive Recursion.Paul Axt - 1965 - Mathematical Logic Quarterly 11 (3):253-255.

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