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
Chapter Title
Second incompleteness theorem: research developments and consequences
Authors
Duccio Pianigiani
Language
English
DOI
10.36253/979-12-215-0778-2.09
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