Authors
Saul Kripke
CUNY Graduate Center
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 Peano 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.
Keywords mathematical incompleteness  independence results  first-order Peano arithmetic  Gentzen  Goodstein
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DOI 10.1080/01445340.2021.1976052
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