The \(\Sigma_1\)-provability logic of \(\mathsf{HA}\)

DOI10.1016/j.apal.2018.05.001zbMath1426.03039arXiv1805.06763OpenAlexW2884919550MaRDI QIDQ720757

Mohammad Ardeshir, Mojtaba Mojtahedi

Publication date: 17 July 2018

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

Full work available at URL: https://arxiv.org/abs/1805.06763

zbMATH Keywords

modal logicdecidabilityHeyting arithmeticintuitionistic logicprovability logicde Jongh property1-completenessarithmetical completeness of GLKripke semantics for intuitionistic normal modal logicprovability interpretation of modality

Mathematics Subject Classification ID

Modal logic (including the logic of norms) (03B45) Metamathematics of constructive systems (03F50) Intuitionistic mathematics (03F55) Provability logics and related algebras (e.g., diagonalizable algebras) (03F45)

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Cites Work

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• The de Jongh property for basic arithmetic
• Intermediate logics and the de Jongh property
• Self-reference and modal logic
• Constructivism in mathematics. An introduction. Volume I
• Provability interpretations of modal logic
• Metamathematical investigation of intuitionistic arithmetic and analysis. With contributions by C. A. Smorynski, J. I. Zucker and W. A. Howard
• Solution of a problem of Leon Henkin
• Arithmetization of metamathematics in a general setting
• The disjunction property implies the numerical existence property
• Reduction of provability logics to Σ₁-provability logics
• On the completenes principle: A study of provability in heyting's arithmetic and extensions
• The interpretability logic of Peano arithmetic
• A Note on Indicator-Functions
• Substitutions of \(\Sigma_1^0\)-sentences: Explorations between intuitionistic propositional logic and intuitionistic arithmetic