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UNFOLDING FINITIST ARITHMETIC

Published online by Cambridge University Press:  11 August 2010

SOLOMON FEFERMAN*
Affiliation:
Stanford University
THOMAS STRAHM*
Affiliation:
University of Bern
*
*DEPARTMENT OF MATHEMATICS, STANFORD UNIVERSITY, STANFORD, CA 94305. E-mail: feferman@stanford.edu
INSTITUT FÜR INFORMATIK UND ANGEWANDTE MATHEMATIK, UNIVERSITÄT BERN, NEUBRÜCKSTRASSE 10, CH-3012 BERN, SWIZTERLAND. E-mail: strahm@iam.unibe.ch

Abstract

The concept of the (full) unfolding of a schematic system is used to answer the following question: Which operations and predicates, and which principles concerning them, ought to be accepted if one has accepted ? The program to determine for various systems of foundational significance was previously carried out for a system of nonfinitist arithmetic, ; it was shown that is proof-theoretically equivalent to predicative analysis. In the present paper we work out the unfolding notions for a basic schematic system of finitist arithmetic, , and for an extension of that by a form of the so-called Bar Rule. It is shown that and are proof-theoretically equivalent, respectively, to Primitive Recursive Arithmetic, , and to Peano Arithmetic, .

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2010

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