The Axiom System IΣ0 Manages to Simultaneously Obey and Evade the Herbrandized Version of the Second Incompleteness Theorem

DOI10.1016/j.entcs.2006.05.047zbMath1262.03122OpenAlexW2028571333WikidataQ114015490 ScholiaQ114015490MaRDI QIDQ4917999

Dan E. Willard

Publication date: 3 May 2013

Published in: Electronic Notes in Theoretical Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.entcs.2006.05.047

zbMATH Keywords

Gödel's second incompleteness theorem\(\mathrm{I}\Sigma_{0}\)

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Gödel numberings and issues of incompleteness (03F40)

Related Items (2)

Passive induction and a solution to a Paris-Wilkie open question ⋮ 2007-2008 Winter Meeting of the Association for Symbolic Logic

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The unprovability of small inconsistency. A study of local and global interpretability
• Faith \& falsity
• On the scheme of induction for bounded arithmetic formulas
• The decision problem for exponential diophantine equations
• Unprovability of consistency statements in fragments of bounded arithmetic
• A generalization of the second incompleteness theorem and some exceptions to it
• Undecidable theories
• Existentially closed structures and Gödel's second incompleteness theorem
• Self-verifying axiom systems, the incompleteness theorem and related reflection principles
• Herbrand consistency and bounded arithmetic
• Solution of a problem of Leon Henkin
• Arithmetization of metamathematics in a general setting
• Cuts, consistency statements and interpretations
• A note on proofs of falsehood
• Gödel's Second incompleteness theorem for Q
• Gödel sentences of bounded arithmetic
• How to extend the semantic tableaux and cut-free versions of the second incompleteness theorem almost to Robinson's arithmetic q
• Automated Reasoning with Analytic Tableaux and Related Methods
• On the Herbrand notion of consistency for finitely axiomatizable fragments of bounded arithmetic theories
• An exploration of the partial respects in which an axiom system recognizing solely addition as a total function can verify its own consistency
• On notation for ordinal numbers
• On Herbrand consistency in weak arithmetic

This page was built for publication: The Axiom System IΣ0 Manages to Simultaneously Obey and Evade the Herbrandized Version of the Second Incompleteness Theorem