Quadratic forms in models of I Δ 0 + Ω 1. I

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Annals of Pure and Applied Logic 148 (1-3):31-48 (2007)
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Abstract

Gauss used quadratic forms in his second proof of quadratic reciprocity. In this paper we begin to develop a theory of binary quadratic forms over weak fragments of Peano Arithmetic, with a view to reproducing Gauss’ proof in this setting

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10.1016/j.apal.2007.05.004

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Citations of this work

Abelian groups and quadratic residues in weak arithmetic.Emil Jeřábek - 2010 - Mathematical Logic Quarterly 56 (3):262-278.
Finitistic Arithmetic and Classical Logic.Mihai Ganea - 2014 - Philosophia Mathematica 22 (2):167-197.

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References found in this work

On the scheme of induction for bounded arithmetic formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (C):261-302.
Existence and feasibility in arithmetic.Rohit Parikh - 1971 - Journal of Symbolic Logic 36 (3):494-508.
Pell equations and exponentiation in fragments of arithmetic.Paola D'Aquino - 1996 - Annals of Pure and Applied Logic 77 (1):1-34.

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