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arXiv · 2102.13141

Mathematical Incompleteness Results in First-Order Peano Arithmetic: A Revisionist View of the Early History

Saul A. Kripke
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Abstract

In the Handbook of Mathematical Logic, the Paris-Harrington variant of Ramsey's theorem is celebrated as the first result of a long 'search' for a purely mathematical incompleteness result in first-order arithmetic. This paper questions the existence of any such search and the status of the Paris-Harrington result as the first mathematical incompleteness result. In fact, I argue that Gentzen gave the first such result, and that it was restated by Goodstein in a number-theoretic form.

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BibTeXRIS

Saul A. Kripke. 2021-02-25. Mathematical Incompleteness Results in First-Order Peano Arithmetic: A Revisionist View of the Early History. https://arxiv.org/abs/2102.13141

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