We start with the central result from which we derive the first Gödel Theorem. That the 1931 proof of the first theorem is syntactic and constructive. This means that it doesn’t appeal to truth and that we concretely give examples of sentences that are independent (neither provable nor refutable). We show Rosser’s version of the first incompleteness theorem. Then we discuss the limit of incompleteness phenomenon and we illustrate a complete and decidable theory. We introduce nonostandard model and we take another look at incompleteness: Tennenbaum’s theorem.
University of Siena, Italy - ORCID: 0000-0001-9441-7226
Titolo del capitolo
First and second Gödel’s theorems and related results
Autori
Duccio Pianigiani
Lingua
Inglese
DOI
10.36253/979-12-215-0778-2.08
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