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Some theories with positive induction of ordinal strength φω0

Published online by Cambridge University Press:  12 March 2014

Gerhard Jäger  and
Thomas Strahm
Gerhard Jäger
Affiliation:
Institut für Informatik und Angewandte Mathematik, Universität Bern, Neubrückstrasse 10, CH-3012 Bern, Switzerland, E-mail: jaeger@iam.unibe.ch
Thomas Strahm
Affiliation:
Institut für Informatik und Angewandte Mathematik, Universität Bern, Neubrückstrasse 10, CH-3012 Bern, Switzerland, E-mail: strahm@iam.unibe.ch
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Abstract

This paper deals with: (i) the theory which results from by restricting induction on the natural numbers to formulas which are positive in the fixed point constants, (ii) the theory BON(μ) plus various forms of positive induction, and (iii) a subtheory of Peano arithmetic with ordinals in which induction on the natural numbers is restricted to formulas which are Σ in the ordinals. We show that these systems have proof-theoretic strength φω0.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 3 , September 1996 , pp. 818 - 842
Copyright
Copyright © Association for Symbolic Logic 1996

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