Herbrand consistency and bounded arithmetic

DOI10.4064/fm171-3-7zbMath0995.03044OpenAlexW2035207489MaRDI QIDQ2773372

Zofia Adamowicz

Publication date: 21 February 2002

Published in: Fundamenta Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/fm171-3-7

zbMATH Keywords

provabilitybounded arithmeticweak arithmeticGödel's incompleteness theoremHerbrand consistency

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Nonstandard models of arithmetic (03H15) Models of arithmetic and set theory (03C62)

Related Items (10)

Well-behaved principles alternative to bounded induction ⋮ Herbrand consistency of some finite fragments of bounded arithmetical theories ⋮ Herbrand consistency of some arithmetical theories ⋮ 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 generalization of the second incompleteness theorem and some exceptions to it ⋮ 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 ⋮ On the available partial respects in which an axiomatization for real valued arithmetic can recognize its consistency

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