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A Hierarchy on the Class of Primitive Recursive Ordinal Functions

Published online by Cambridge University Press:  20 November 2018

Stanley H. Stahl
Stanley H. Stahl*
Affiliation:
Westfield State College, West field, Massachusetts; Trinity College, Hartford, Connecticut
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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).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 6 , 01 December 1976 , pp. 1205 - 1209
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Grzegorczyk, A., Some classes of recursive functions, Rozprawy Matematyczne IV (1953), 4–45.Google Scholar
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. Platek, R. A., Foundations of recursion theory, Ph.D. dissertation and unpublished supplement, Stanford University 1966.Google Scholar
4. Stahl, S. H., Classes of primitive recursive ordinal functions, Ph.D. dissertation, University of Michigan, 1974.Google Scholar
5. Yasuhara, A., Recursive function theory and logic (Academic Press, New York, 1971).Google Scholar