A proof theory for the logic of provability in true arithmetic

DOI10.1007/S11225-019-09891-0zbMath1462.03027OpenAlexW2996029277WikidataQ126538805 ScholiaQ126538805MaRDI QIDQ2193977

Hirohiko Kushida

Publication date: 25 August 2020

Published in: Studia Logica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11225-019-09891-0

zbMATH Keywords

proof theoryprovability logiccut-eliminationtrue arithmetic

Mathematics Subject Classification ID

Modal logic (including the logic of norms) (03B45) Cut-elimination and normal-form theorems (03F05) First-order arithmetic and fragments (03F30) Provability logics and related algebras (e.g., diagonalizable algebras) (03F45)

Cites Work

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• Cut elimination for GLS using the terminability of its regress process
• The modal logic of Gödel sentences
• The modal logic of provability: cut-elimination
• On some proof theoretical properties of the modal logic GL
• The modal logic of provability. The sequential approach
• Proof theory. 2nd ed
• Provability interpretations of modal logic
• An effective fixed-point theorem in intuitionistic diagonalizable algebras. (The algebraization of the theories which express Theor. IX.)
• Explicit Provability and Constructive Semantics
• VALENTINI’S CUT-ELIMINATION FOR PROVABILITY LOGIC RESOLVED
• On modal systems having arithmetical interpretations

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