Independent sentences of mathematical character Duccio Pianigiani University of Siena, Italy This is a section of Lectures in Proof Theory and Complexity(DOI: 10.36253/979-12-215-0778-2) by Duccio Pianigiani Firenze University Press, USiena Press Florence 2025 https://doi.org/10.36253/979-12-215-0778-2.11

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The reception of incompleteness results within the mathematical community was very slow. One reason for the large underestimation of gödelians’ results in part of the community of mathematicians, which helped to brake their assimilation, was linked to the metamathematical character of the statement “I am not provable” used in the constructive proof. The perceived distance from the concrete mathematical work is perhaps behind the most striking case of the silence in this regard: that of the the French group ‘Bourbaki’ of formalists mathematicians. For this reason, in an attempt to address these objections, some scholars have devoted themselves to the search for independent statements of mathematical content, with proofs that did not rely on the typical Gödelian toolbox.

 Paris-Harrington theorem Ramsey theorems Hydra Game Goodstein sequences

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