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Plain Bases for Classes of Primitive Recursive Functionsby: Stefano Mazzanti
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AbstractAbasisforaset 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 ℰn with n ge 3. Such results are then applied in order to show that ℰn+1 = Kn for n ge 2, where Knnisinℕ is the Axt hierarchy.
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