Geodesic
A Hierarchy on the Class of Primitive Recursive Ordinal Functions
Canadian journal of mathematics, Tome 28 (1976) no. 6, pp. 1205-1209

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The class of primitive recursive ordinal functions (PR) has been studied recently by numerous recursion theorists and set theorists (see, for example, Platek [3] and Jensen-Karp [2]). These investigations have been part of an inquiry concerning a larger class of functions; in Platek's case, the class of ordinal recursive functions and in the case of Jensen and Karp, the class of primitive recursive set functions. In [4] I began to study PR in depth and this paper is a report on an attractive analogy between PR and its progenitor, the class of primitive recursive functions on the natural numbers (Prim. Rec). 
Stahl, Stanley H. A Hierarchy on the Class of Primitive Recursive Ordinal Functions. Canadian journal of mathematics, Tome 28 (1976) no. 6, pp. 1205-1209. doi: 10.4153/CJM-1976-120-3
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[1] 1. Grzegorczyk, A., Some classes of recursive functions, Rozprawy Matematyczne IV (1953), 4–45. Google Scholar

[2] 2. Jensen, R. and Karp, C., Primitive recursive set functions, in D. Scott (éd.), Axiomatic set theory (Amer. Math. Soc, Providence, R.I., 1971), 143–176. Google Scholar

[3] 3. Platek, R. A., Foundations of recursion theory, Ph.D. dissertation and unpublished supplement, Stanford University 1966. Google Scholar

[4] 4. Stahl, S. H., Classes of primitive recursive ordinal functions, Ph.D. dissertation, University of Michigan, 1974. Google Scholar

[5] 5. Yasuhara, A., Recursive function theory and logic (Academic Press, New York, 1971). Google Scholar

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