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Number theory and elementary arithmetic
Philosophia Mathematica 11 (3):257-284 (2003)
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 contextAuthor's Profile
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Citations of this work
Szemerédi’s theorem: An exploration of impurity, explanation, and content.Patrick J. Ryan - 2023 - Review of Symbolic Logic 16 (3):700-739.
What does it take to prove fermat's last theorem? Grothendieck and the logic of number theory.Colin McLarty - 2010 - Bulletin of Symbolic Logic 16 (3):359-377.
Hilbert's program then and now.Richard Zach - 2002 - In Dale Jacquette (ed.), Philosophy of Logic. Malden, Mass.: North Holland. pp. 411–447.
Understanding, formal verification, and the philosophy of mathematics.Jeremy Avigad - 2010 - Journal of the Indian Council of Philosophical Research 27:161-197.
References found in this work
Does mathematics need new axioms.Solomon Feferman, Harvey M. Friedman, Penelope Maddy & John R. Steel - 1999 - Bulletin of Symbolic Logic 6 (4):401-446.
Two applications of logic to mathematics.Gaisi Takeuti - 1978 - [Princeton, N.J.]: Princeton University Press.
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