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About the proof-theoretic ordinals of weak fixed point theories

Published online by Cambridge University Press:  12 March 2014

Gerhard Jäger  and
Barbara Primo
Gerhard Jäger
Affiliation:
Institut für Informatik und Angewandte Mathematik, Universität Bern, 3012 Bern, Switzerland, E-mail: jaeger@iam.unibe.ch
Barbara Primo
Affiliation:
Mathematics Department, Eidgenössische Technische Hochschule, 8092 Zurich, Switzerland
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Abstract

This paper presents several proof-theoretic results concerning weak fixed point theories over second order number theory with arithmetic comprehension and full or restricted induction on the natural numbers. It is also shown that there are natural second order theories which are proof-theoretically equivalent but have different proof-theoretic ordinals.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 3 , September 1992 , pp. 1108 - 1119
Copyright
Copyright © Association for Symbolic Logic 1992

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References

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