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The next admissible set1

Published online by Cambridge University Press:  12 March 2014

K. J. Barwise ,
R. O. Gandy  and
Y. N. Moschovakis
K. J. Barwise
Affiliation:
University of Wisconsin, Madison
R. O. Gandy
Affiliation:
Oxford University
Y. N. Moschovakis
Affiliation:
University of California, Los Angeles
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Extract

In this paper we describe generalizations of several approaches to the hyperarithmetic hierarchy, show how they are related to the Kripke-Platek theory of admissible ordinals and sets, and study conditions under which the various approaches remain equivalent.

To put matters in some perspective, let us first review various approaches to the theory of hyperarithmetic sets. For most purposes, it is convenient to first define the semi-hyperarithmetic (semi-HA) subsets of N. A set is then said to be hyperarithmetic (HA) if both it and its complement are semi-HA. A total number-theoretic function is HA if its graph is HA.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 36 , Issue 1 , March 1971 , pp. 108 - 120
Copyright
Copyright © Association for Symbolic Logic 1971

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Footnotes

1

Most of the results of this paper were obtained during the spring of 1968 while Barwise and Gandy were attending the UCLA Logic Year, the first as an NSF Postdoctoral Fellow, the second as Visiting Associate Professor. They record here their gratitude to the Mathematics Department of UCLA for its gracious hospitality. The research of Barwise and Moschovakis was also supported in part by NSF Grants.

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