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Second incompleteness theorem: research developments and consequences

  • Duccio Pianigiani

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.

  • Keywords:
  • Derivability conditions,
  • consisteny,
  • Turing’s progressions,
  • Provability Logic,
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Duccio Pianigiani

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

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Chapter Information

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

CC BY-SA 4.0

Metadata License

CC0 1.0

Bibliographic Information

Book Title

Lectures in Proof Theory and Complexity

Authors

Duccio Pianigiani

Peer Reviewed

Publication Year

2025

Copyright Information

© 2025 Author(s)

Content License

CC BY-SA 4.0

Metadata License

CC0 1.0

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

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3035-5915

Series E-ISSN

3035-5931

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