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
Chapter Title
First and second Gödel’s theorems and related results
Authors
Duccio Pianigiani
Language
English
DOI
10.36253/979-12-215-0778-2.08
Peer Reviewed
Publication Year
2025
Copyright Information
© 2025 Author(s)
Content License
Metadata License
Book Title
Lectures in Proof Theory and Complexity
Authors
Duccio Pianigiani
Peer Reviewed
Publication Year
2025
Copyright Information
© 2025 Author(s)
Content License
Metadata License
Publisher Name
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
Series Title
UNIverSI. Ricerca e Didattica all’Università di Siena
Series ISSN
3035-5915
Series E-ISSN
3035-5931