Unfolding finitist arithmetic

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

Predicativity and Feferman.Laura Crosilla - 2017 - In Gerhard Jäger & Wilfried Sieg (eds.), Feferman on Foundations: Logic, Mathematics, Philosophy. Cham: Springer. pp. 423-447.
Truth, Pretense and the Liar Paradox.Bradley Armour-Garb & James A. Woodbridge - 2015 - In T. Achourioti, H. Galinon, J. Martínez Fernández & K. Fujimoto (eds.), Unifying the Philosophy of Truth. Dordrecht: Imprint: Springer. pp. 339-354.
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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