Unary primitive recursive functions

Journal of Symbolic Logic 73 (4):1122-1138 (2008)

Abstract
In this article, we study some new characterizations of primitive recursive functions based on restricted forms of primitive recursion, improving the pioneering work of R. M. Robinson and M. D. Gladstone. We reduce certain recursion schemes (mixed/pure iteration without parameters) and we characterize one-argument primitive recursive functions as the closure under substitution and iteration of certain optimal sets
Keywords unary   primitive recursive   recursion scheme   reduction
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DOI 10.2178/jsl/1230396909
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References found in this work BETA

Some Classes of Recursive Functions.Andrzej Grzegorczyk - 1955 - Journal of Symbolic Logic 20 (1):71-72.
On the Algebraic Structure of Primitive Recursive Functions.István Szalkai - 1985 - Mathematical Logic Quarterly 31 (35‐36):551-556.
Bounded Iteration and Unary Functions.Stefano Mazzanti - 2005 - Mathematical Logic Quarterly 51 (1):89-94.
Simplifications of the Recursion Scheme.M. D. Gladstone - 1971 - Journal of Symbolic Logic 36 (4):653-665.

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Citations of this work BETA

Iteration on Notation and Unary Functions.Stefano Mazzanti - 2013 - Mathematical Logic Quarterly 59 (6):415-434.

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