Consistency statements and iterations of computable functions in \(\mathrm{I}\Sigma_1\) and PRA

DOI10.1007/S00153-010-0199-2zbMath1201.03054OpenAlexW2093589140WikidataQ120640954 ScholiaQ120640954MaRDI QIDQ711565

Joost J. Joosten

Publication date: 27 October 2010

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00153-010-0199-2

zbMATH Keywords

computable functionsconservativityarithmetical theoriesconsistency statementsdefinable cuts

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Models of arithmetic and set theory (03C62) Recursive functions and relations, subrecursive hierarchies (03D20)

Cites Work

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• On the scheme of induction for bounded arithmetic formulas
• Induction rules, reflection principles, and provably recursive functions
• Proof-theoretic analysis by iterated reflection
• Saturated models of universal theories
• Quantifier-free and one-quantifier systems
• The closed fragment of the interpretability logic of PRA with a constant for I\(\Sigma^1\)
• Herbrand analyses
• Grundlagen der Mathematik I
• Existence and feasibility in arithmetic
• On n-quantifier induction
• Notes on polynomially bounded arithmetic
• Proof theory

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