The interpretability logic of Peano arithmetic

DOI10.2307/2274474zbMath0725.03037OpenAlexW2016617619MaRDI QIDQ5202653

Alessandro Berarducci

Publication date: 1990

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

Full work available at URL: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.99.2157

zbMATH Keywords

modal logicPeano Arithmeticaxiomatizationdecision procedureZermelo-Fraenkel Set Theoryaxiomatic treatment of interpretability

Mathematics Subject Classification ID

Modal logic (including the logic of norms) (03B45) First-order arithmetic and fragments (03F30) Models of arithmetic and set theory (03C62) Relative consistency and interpretations (03F25)

Related Items (28)

On modal logics of model-theoretic relations ⋮ On strong provability predicates and the associated modal logics ⋮ Franco Montagna's work on provability logic and many-valued logic ⋮ A simple proof of arithmetical completeness for \(\Pi_ 1\)-conservativity logic ⋮ Hard provability logics ⋮ Interpretability suprema in Peano arithmetic ⋮ Modal completeness of sublogics of the interpretability logic IL ⋮ Lewis meets Brouwer: constructive strict implication ⋮ Theory and application of labelling techniques for interpretability logics ⋮ Bisimulations and bisimulation games between Verbrugge models ⋮ TWO NEW SERIES OF PRINCIPLES IN THE INTERPRETABILITY LOGIC OF ALL REASONABLE ARITHMETICAL THEORIES ⋮ Transductions in arithmetic ⋮ A short note on essentially \(\Sigma_1\) sentences ⋮ Provability and interpretability logics with restricted realizations ⋮ Undecidability in diagonalizable algebras ⋮ The formalization of interpretability ⋮ The de Jongh property for basic arithmetic ⋮ INTERPRETABILITY LOGICS AND GENERALISED VELTMAN SEMANTICS ⋮ A generalized notion of weak interpretability and the corresponding modal logic ⋮ The provability logic for \(\Sigma_ 1\)-interpolability ⋮ The logic of linear tolerance ⋮ The \(\Sigma_1\)-provability logic of \(\mathsf{HA}\) ⋮ Interpretability over peano arithmetic ⋮ Filtrations of generalized Veltman models ⋮ Interpretability in PRA ⋮ The closed fragment of the interpretability logic of PRA with a constant for I\(\Sigma^1\) ⋮ On the limit existence principles in elementary arithmetic and \(\varSigma_{n}^{0}\)-consequences of theories ⋮ HIERARCHICAL INCOMPLETENESS RESULTS FOR ARITHMETICALLY DEFINABLE EXTENSIONS OF FRAGMENTS OF ARITHMETIC

Cites Work

• Self-reference and modal logic
• Provability interpretations of modal logic

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