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Wellordering proofs for metapredicative Mahlo

Published online by Cambridge University Press:  12 March 2014

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

In this article we provide wellordering proofs for metapredicative systems of explicit mathematics and admissible set theory featuring suitable axioms about the Mahloness of the underlying universe of discourse. In particular, it is shown that in the corresponding theories EMA of explicit mathematics and KPm0 of admissible set theory, transfinite induction along initial segments of the ordinal φω00, for φ being a ternary Veblen function, is derivable. This reveals that the upper bounds given for these two systems in the paper Jäger and Strahm [11] are indeed sharp.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 1 , March 2002 , pp. 260 - 278
Copyright
Copyright © Association for Symbolic Logic 2002

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