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Independent sentences of mathematical character

  • Duccio Pianigiani

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.

  • Keywords:
  • Paris-Harrington theorem,
  • Ramsey theorems,
  • Hydra Game,
  • Goodstein sequences,
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Duccio Pianigiani

University of Siena, Italy - ORCID: 0000-0001-9441-7226

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  • Anno di pubblicazione: 2025
  • Pagine: 155-172

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  • Anno di pubblicazione: 2025

Informazioni sul capitolo

Titolo del capitolo

Independent sentences of mathematical character

Autori

Duccio Pianigiani

Lingua

English

DOI

10.36253/979-12-215-0778-2.11

Opera sottoposta a peer review

Anno di pubblicazione

2025

Copyright

© 2025 Author(s)

Licenza d'uso

CC BY-SA 4.0

Licenza dei metadati

CC0 1.0

Informazioni bibliografiche

Titolo del libro

Lectures in Proof Theory and Complexity

Autori

Duccio Pianigiani

Opera sottoposta a peer review

Anno di pubblicazione

2025

Copyright

© 2025 Author(s)

Licenza d'uso

CC BY-SA 4.0

Licenza dei metadati

CC0 1.0

Editore

Firenze University Press, USiena Press

DOI

10.36253/979-12-215-0778-2

eISBN (pdf)

979-12-215-0778-2

eISBN (xml)

979-12-215-0779-9

Collana

UNIverSI. Ricerca e Didattica all’Università di Siena

ISSN della collana

3035-5915

e-ISSN della collana

3035-5931

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