Mathematical Incompleteness Results in First-Order Peano Arithmetic: A Revisionist View of the Early History (2022)
Kripke, Saul A. (Author)
History and Philosophy of Logic
Volume: 43
Issue: 2
Pages: 175-182
Publication date: 2022
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.
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