On modal systems having arithmetical interpretations

DOI10.2307/2274147zbMath0587.03016OpenAlexW2052270606MaRDI QIDQ3714054

Arnon Avron

Publication date: 1984

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

Full work available at URL: https://doi.org/10.2307/2274147

zbMATH Keywords

semanticsprovabilitycut-eliminationdisjunction propertysequential calculusmodal logic GLmodal logic Grzfirst-order modal system QGLomitting system

Mathematics Subject Classification ID

Modal logic (including the logic of norms) (03B45) Cut-elimination and normal-form theorems (03F05)

Related Items (16)

VALENTINI’S CUT-ELIMINATION FOR PROVABILITY LOGIC RESOLVED ⋮ On arithmetical completeness of the logic of proofs ⋮ Positive modal logic ⋮ An Arithmetically Complete Predicate Modal Logic ⋮ On the proof-theory of two formalisations of modal first-order logic ⋮ A New Arithmetically Incomplete First-Order Extension of Gl All Theorems of Which Have Cut Free Proofs ⋮ A proof theory for the logic of provability in true arithmetic ⋮ Interacting explicit evidence systems ⋮ Explicit Provability and Constructive Semantics ⋮ Sequent calculi for intuitionistic Gödel-Löb logic ⋮ Kripke Semantics for Basic Sequent Systems ⋮ Unnamed Item ⋮ The bounded proof property via step algebras and step frames ⋮ NON-WELL-FOUNDED PROOFS FOR THE GRZEGORCZYK MODAL LOGIC ⋮ The modal logic of provability: cut-elimination ⋮ Introduction: Non-classical Logics—Between Semantics and Proof Theory (In Relation to Arnon Avron’s Work)

Cites Work

• A modal sequent calculus for a fragment of arithmetic
• Fifty years of self-reference in arithmetic
• Provability interpretations of modal logic

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