Unary primitive recursive functions

Journal of Symbolic Logic 73 (4):1122-1138 (2008)
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
Nadejda V. Georgieva (1976). Classes of One-Argument Recursive Functions. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 22 (1):127-130.
István Szalkai (1985). On the Algebraic Structure of Primitive Recursive Functions. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (35-36):551-556.
Stefano Mazzanti (2005). Bounded Iteration and Unary Functions. Mathematical Logic Quarterly 51 (1):89-94.
G. Germano & S. Mazzanti (1988). Primitive Iteration and Unary Functions. Annals of Pure and Applied Logic 40 (3):217-256.

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

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