Iterated local reflection versus iterated consistency

DOI10.1016/0168-0072(95)00007-4zbMath0848.03031OpenAlexW1974965205MaRDI QIDQ1899141

Lev D. Beklemishev

Publication date: 27 October 1996

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

Full work available at URL: https://doi.org/10.1016/0168-0072(95)00007-4

zbMATH Keywords

provabilityPRAiterated reflectioniterated consistencynice well-orderingssmooth numerationstransfinite progression

Mathematics Subject Classification ID

Second- and higher-order arithmetic and fragments (03F35) Recursive ordinals and ordinal notations (03F15)

Related Items

Evitable iterates of the consistency operator, Slow reflection, The logic of Turing progressions, The omega-rule interpretation of transfinite provability logic, Classes and truths in set theory, Reflection calculus and conservativity spectra, Parameter free induction and provably total computable functions, ON THE INEVITABILITY OF THE CONSISTENCY OPERATOR, Turing-Taylor expansions for arithmetic theories, Transfinite Progressions: A Second Look at Completeness, Principles for object-linguistic consequence: from logical to irreflexive, A note on the consistency operator, On the limit existence principles in elementary arithmetic and \(\varSigma_{n}^{0}\)-consequences of theories, REFLECTION RANKS AND ORDINAL ANALYSIS

Cites Work

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• Fragments of arithmetic
• Provability logics for natural Turing progressions of arithmetical theories
• The formalization of interpretability
• On bimodal logics of provability
• Solution of a problem of Leon Henkin
• Reflection principles and iterated consistency assertions
• Reflection Principles and their Use for Establishing the Complexity of Axiomatic Systems
• Transfinite recursive progressions of axiomatic theories
• Systems of Logic Based on Ordinals^†