Number theory and elementary arithmetic

Philosophia Mathematica 11 (3):257-284 (2003)
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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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10.1093/philmat/11.3.257

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Jeremy Avigad
Carnegie Mellon University

Citations of this work

Reliability of mathematical inference.Jeremy Avigad - 2020 - Synthese 198 (8):7377-7399.
Hilbert’s Program.Richard Zach - 2012 - In Ed Zalta, Stanford Encyclopedia of Philosophy. Stanford, CA: Stanford Encyclopedia of Philosophy.
Hilbert's program then and now.Richard Zach - 2002 - In Dale Jacquette, Philosophy of Logic. Malden, Mass.: North Holland. pp. 411–447.

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References found in this work

Introduction to metamathematics.Stephen Cole Kleene - unknown - Groningen: P. Noordhoff N.V..
Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
Finitism.W. W. Tait - 1981 - Journal of Philosophy 78 (9):524-546.

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