We discuss the Second incompleteness theorem, some research developments and consequences. We introduce Turing’s progressions as attempt to attempt to overcome the problem of incompleteness. The we introduce the basics of classical and intuitionistic Provability Logic and some recent developments. Lastly we provide a guide to consistency proofs of arithmetic developed by Gentzen and Schütte.
University of Siena, Italy - ORCID: 0000-0001-9441-7226
Titolo del capitolo
Second incompleteness theorem: research developments and consequences
Autori
Duccio Pianigiani
Lingua
English
DOI
10.36253/979-12-215-0778-2.09
Opera sottoposta a peer review
Anno di pubblicazione
2025
Copyright
© 2025 Author(s)
Licenza d'uso
Licenza dei metadati
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
Licenza dei metadati
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