# Number theory and elementary arithmetic

@article{Avigad2003NumberTA, title={Number theory and elementary arithmetic}, author={Jeremy Avigad}, journal={Philosophia Mathematica}, year={2003}, volume={11}, pages={257-284} }

Elementary arithmetic (also known as “elementary function arithmetic”) is a fragment of first-order arithmetic so weak that it cannot prove the totality of an iterated exponential function. Surprisingly, however, the theory turns out to be 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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