Unprovability of consistency statements in fragments of bounded arithmetic

DOI10.1016/0168-0072(94)00049-9zbMath0834.03022OpenAlexW2071977753MaRDI QIDQ1896613

Samuel R. Buss, Aleksandar Ignjatović

Publication date: 31 March 1996

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-0072(94)00049-9

zbMATH Keywords

bounded arithmeticbootstrappingweak fragments of arithmeticinduction schemasinduction-free fragmentsunprovability of bounded consistency

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30)

Related Items (9)

Proving consistency of equational theories in bounded arithmetic ⋮ 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 ⋮ A model of \(\widehat{R}^2_3\) inside a subexponential time resource ⋮ A generalization of the second incompleteness theorem and some exceptions to it ⋮ CONSISTENCY PROOF OF A FRAGMENT OF PV WITH SUBSTITUTION IN BOUNDED ARITHMETIC ⋮ Some specially formulated axiomizations for \(\mathrm{I}\Sigma _0\) manage to evade the Herbrandized version of the second incompleteness theorem ⋮ 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

Cites Work

• A note on bounded arithmetic
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