Axiomatizing provable \(n\)-provability

DOI10.1134/S1064562418070153zbMath1484.03123OpenAlexW2963720101MaRDI QIDQ1732059

E. A. Kolmakov, Lev D. Beklemishev

Publication date: 15 March 2019

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562418070153

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Provability logics and related algebras (e.g., diagonalizable algebras) (03F45)

Cites Work

• Self-reference and modal logic
• Proof-theoretic analysis by iterated reflection
• Provability algebras and proof-theoretic ordinals. I
• Parameter free induction and provably total computable functions
• Unprovability and proving unprovability
• On the limit existence principles in elementary arithmetic and \(\varSigma_{n}^{0}\)-consequences of theories
• Reflection principles and provability algebras in formal arithmetic
• On strong provability predicates and the associated modal logics
• Reflection Principles and their Use for Establishing the Complexity of Axiomatic Systems
• Transfinite recursive progressions of axiomatic theories
• Systems of Logic Based on Ordinals^†

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