On the Herbrand notion of consistency for finitely axiomatizable fragments of bounded arithmetic theories

DOI10.2178/jsl/1146620163zbMath1099.03050OpenAlexW1997679513MaRDI QIDQ5480630

Leszek Aleksander Kołodziejczyk

Publication date: 3 August 2006

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2178/jsl/1146620163

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30)

Related Items (7)

Herbrand consistency of some finite fragments of bounded arithmetical theories ⋮ Restricted polynomial induction versus parameter free ordinary induction ⋮ Herbrand consistency of some arithmetical theories ⋮ Restricted polynomial induction versus ordinary induction ⋮ Passive induction and a solution to a Paris-Wilkie open question ⋮ The Axiom System IΣ0 Manages to Simultaneously Obey and Evade the Herbrandized Version of the Second Incompleteness Theorem ⋮ Some specially formulated axiomizations for \(\mathrm{I}\Sigma _0\) manage to evade the Herbrandized version of the second incompleteness theorem

Cites Work

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• On the scheme of induction for bounded arithmetic formulas
• Unprovability of consistency statements in fragments of bounded arithmetic
• Herbrand consistency and bounded arithmetic
• How to extend the semantic tableaux and cut-free versions of the second incompleteness theorem almost to Robinson's arithmetic q
• On Herbrand consistency in weak arithmetic

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