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Constructively accessible ordinal numbers1

Published online by Cambridge University Press:  12 March 2014

Wayne Richter
Wayne Richter*
Affiliation:
Rutgers, The State University
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Extract

In [11] the constructive ordinals were extended to constructive finite number classes by using systems of notations where mappings at limit ordinals are just partial recursive functions. It turned out that these systems are equivalent, both in terms of ordinals represented and the forms of the sets of notations, to extensions obtained by using mappings at limit ordinals which are partial recursive in (sets of notations for) previously defined number classes. In this article these results are extended to constructive transfinite number classes. We present a system (F, ||) which, in terms of our analogy with the classical ordinals, provides notations for the ordinals less than the first “constructively inaccessible” ordinal, and show that the above equivalence holds at least this far.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 1 , 26 April 1968 , pp. 43 - 55
Copyright
Copyright © Association for Symbolic Logic 1968

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Footnotes

1

Most of the results presented here were announced without proof in [12]. Research of the author was begun while he held a National Science Foundation Predoctoral fellowship. Some of the material appeared in [10]. The research was continued at Dartmouth College in the summer of 1964, supported by National Science Foundation Grant G23805.

References

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