Article ID: CBB257161891

Mathematical Incompleteness Results in First-Order Peano Arithmetic: A Revisionist View of the Early History (2022)

unapi

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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https://data.isiscb.org/isis/citation/CBB257161891/

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Authors & Contributors
Luciano, Erika
Vrhovski, Jan
Nobrega, Hugo
Kennedy, Juliette
Viana, Petrucio
Cerioli, Márcia R.
Concepts
Logic
Philosophy of mathematics
Mathematics
Philosophy
Incompleteness theorems
Number theory; number concept
Time Periods
20th century, early
19th century
20th century
Places
Germany
Poland
North America
Italy
France
Europe
Institutions
Tsinghua University
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