The unprovability of small inconsistency. A study of local and global interpretability

DOI10.1007/BF01387407zbMath0795.03080MaRDI QIDQ688510

Albert Visser

Publication date: 9 December 1993

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

zbMATH Keywords

interpretabilityinconsistencylength of prooffinitely axiomatized theorysequential theoryTunneling Theorem

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Complexity of proofs (03F20) Relative consistency and interpretations (03F25)

Related Items (17)

Friedman-reflexivity ⋮ Passive induction and a solution to a Paris-Wilkie open question ⋮ The small‐is‐very‐small principle ⋮ Transductions in arithmetic ⋮ Interpretability degrees of finitely axiomatized sequential theories ⋮ Sufficient conditions for cut elimination with complexity analysis ⋮ Pairs, sets and sequences in first-order theories ⋮ Peano Corto and Peano Basso: A Study of Local Induction in the Context of Weak Theories ⋮ The Axiom System IΣ0 Manages to Simultaneously Obey and Evade the Herbrandized Version of the Second Incompleteness Theorem ⋮ Rules and arithmetics ⋮ Faith \& falsity ⋮ A generalization of the second incompleteness theorem and some exceptions to it ⋮ No escape from Vardanyan's theorem ⋮ Some specially formulated axiomizations for \(\mathrm{I}\Sigma _0\) manage to evade the Herbrandized version of the second incompleteness theorem ⋮ The Interpretation Existence Lemma ⋮ The role of quantifier alternations in cut elimination ⋮ The arithmetics of a theory

Cites Work

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• On the scheme of induction for bounded arithmetic formulas
• The computational complexity of logical theories
• Cuts, consistency statements and interpretations
• A note on proofs of falsehood
• Some Prime Elements in the Lattice of Interpretability Types
• Existence and feasibility in arithmetic

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