Number theory and elementary arithmetic

Philosophia Mathematica 11 (3):257-284 (2003)

Authors
Jeremy Avigad
Carnegie Mellon University
Abstract
is a fragment of first-order aritlimetic so weak that it cannot prove the totality of an iterated exponential fimction. Surprisingly, however, the theory is remarkably robust. I will discuss formal results that show that many theorems of number theory and combinatorics are derivable in elementary arithmetic, and try to place these results in a broader philosophical context
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DOI 10.1093/philmat/11.3.257
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References found in this work BETA

Subsystems of Second-Order Arithmetic.Stephen G. Simpson - 2004 - Studia Logica 77 (1):129-129.
Introduction to Metamathematics.Stephen Cole Kleene - 1954 - Journal of Symbolic Logic 19 (3):215-216.
Introduction to Metamathematics.Stephen Cole Kleene - 1968 - Journal of Symbolic Logic 33 (2):290-291.

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Citations of this work BETA

Hilbert's Program Then and Now.Richard Zach - 2007 - In Dale Jacquette (ed.), Philosophy of Logic. Amsterdam: North Holland. pp. 411–447.
The Metamathematics of Ergodic Theory.Jeremy Avigad - 2009 - Annals of Pure and Applied Logic 157 (2-3):64-76.
More Infinity for a Better Finitism.Sam Sanders - 2010 - Annals of Pure and Applied Logic 161 (12):1525-1540.

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