Provability algebras and proof-theoretic ordinals. I

DOI10.1016/j.apal.2003.11.030zbMath1048.03045OpenAlexW1994332324MaRDI QIDQ1877092

Lev D. Beklemishev

Publication date: 16 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.apal.2003.11.030

zbMATH Keywords

Peano arithmeticprovability logicproof-theoretic ordinal analysisprovability algebra

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Other algebras related to logic (03G25) Recursive ordinals and ordinal notations (03F15) Provability logics and related algebras (e.g., diagonalizable algebras) (03F45)

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Cites Work

• Provability interpretations of modal logic
• Wie die Beweistheorie zu ihren Ordinalzahlen kam und kommt
• A proof-theoretic analysis of collection
• Induction rules, reflection principles, and provably recursive functions
• Proof-theoretic analysis by iterated reflection
• On the induction schema for decidable predicates
• On strong provability predicates and the associated modal logics
• Deduction-preserving "Recursive Isomorphisms" between theories
• Systems of Logic Based on Ordinals^†
• Subrecursive degrees and fragments of Peano arithmetic
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