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JEREMY AVIGAD, Number theory and elementary arithmetic, Philosophia Mathematica, Volume 11, Issue 3, October 2003, Pages 257–284, https://doi.org/10.1093/philmat/11.3.257
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Abstract
Elementary arithmetic (also known as ‘elementary function arithmetic’) 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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©2003 PHILOSOPHIA MATHEMATICA
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