Date of Original Version

6-19-2002

Type

Technical Report

Rights Management

All Rights Reserved

Abstract or Table of Contents

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.

Comments

CMU-PHIL-134

Included in

Philosophy Commons

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