Review of Symbolic Logic 3 (4):665-689 (2010)

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,
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DOI 10.1017/s1755020310000183
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References found in this work BETA

Finitism.W. W. Tait - 1981 - Journal of Philosophy 78 (9):524-546.
Fragments of Arithmetic.Wilfried Sieg - 1983 - Annals of Pure and Applied Logic 28 (1):33-71.

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Citations of this work BETA

A Feasible Theory of Truth Over Combinatory Algebra.Sebastian Eberhard - 2014 - Annals of Pure and Applied Logic 165 (5):1009-1033.

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