Number theory and elementary arithmetic

title={Number theory and elementary arithmetic},
journal={Philosophia Mathematica},
year={2003},
volume={11},
pages={257-284}
}
• Published 1 October 2003
• Mathematics
• Philosophia Mathematica
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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