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Russian Mathematical Surveys, 2005, Volume 60, Issue 2, Pages 197–268
DOI: https://doi.org/10.1070/RM2005v060n02ABEH000823 (Mi rm1401) 		 
This article is cited in 79 scientific papers (total in 79 papers)

Reflection principles and provability algebras in formal arithmetic

L. D. Beklemishev

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (718 kB) Citations (79) Russian version article
References:
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DOI: https://doi.org/10.1070/RM2005v060n02ABEH000823
Abstract: This paper is a study of reflection principles in fragments of formal Peano arithmetic and their applications to the comparison and classification of arithmetical theories.
Received: 11.01.2005
Bibliographic databases:
Document Type: Article
UDC: 510.23
MSC: Primary 03F45, 03F15, 03F30; Secondary 03F05, 03F40
Language: English
Original paper language: Russian
Citation: L. D. Beklemishev, “Reflection principles and provability algebras in formal arithmetic”, Russian Math. Surveys, 60:2 (2005), 197–268
Citation in format AMSBIB
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\by L.~D.~Beklemishev
\paper Reflection principles and provability algebras in~formal arithmetic
\jour Russian Math. Surveys
\yr 2005
\vol 60
\issue 2
\pages 197--268
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Linking options:
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  • https://doi.org/10.1070/RM2005v060n02ABEH000823
  • https://www.mathnet.ru/eng/rm/v60/i2/p3
    • This publication is cited in the following 79 articles:
    1. Izv. Math., 89:1 (2025), 1–14  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    2. Andrés Cordón-Franco, F. Félix Lara-Martín, “Semi-honest subrecursive degrees and the collection rule in arithmetic”, Arch. Math. Logic, 63:1-2 (2024), 163  crossref
    3. Piotr Gruza, Mateusz Łełyk, “Varieties of truth definitions”, Arch. Math. Logic, 2024  crossref
    4. EVGENY A. KOLMAKOV, “ON SHAVRUKOV'S NON-ISOMORPHISM THEOREM FOR DIAGONALIZABLE ALGEBRAS”, The Review of Symbolic Logic, 17:1 (2024), 206  crossref
    5. Haruka Kogure, Taishi Kurahashi, “On the conservation results for local reflection principles”, Journal of Logic and Computation, 2024  crossref
    6. L. V. Dvorkin, “On provability logics of Niebergall arithmetic”, Izv. Math., 88:3 (2024), 468–505  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. Leszek Aleksander Kołodziejczyk, Tin Lok Wong, Keita Yokoyama, “Ramsey's theorem for pairs, collection, and proof size”, J. Math. Log., 24:02 (2024)  crossref
    8. Luca Castaldo, Maciej Głowacki, “Implicit commitments of instrumental acceptance: A case study”, The Philosophical Quarterly, 2024  crossref
    9. Maciej Głowacki, Mateusz Łełyk, “Reflecting on believability: on the epistemic approach to justifying implicit commitments”, Philos Stud, 2024  crossref
    10. ALI ENAYAT, MATEUSZ ŁEŁYK, “AXIOMATIZATIONS OF PEANO ARITHMETIC: A TRUTH-THEORETIC VIEW”, J. symb. log., 88:4 (2023), 1526  crossref
    11. Mateusz ŁeŁyk, Carlo Nicolai, “Implicit commitment in a general setting”, Journal of Logic and Computation, 2023  crossref
    12. James Walsh, “Evitable iterates of the consistency operator”, COM, 12:1 (2023), 59  crossref
    13. Paulo Guilherme Santos, Wilfried Sieg, Reinhard Kahle, “A new perspective on completeness and finitist consistency”, Journal of Logic and Computation, 2023  crossref
    14. James Walsh, “Characterizations of ordinal analysis”, Annals of Pure and Applied Logic, 174:4 (2023), 103230  crossref
    15. MATEUSZ ZBIGNIEW ŁEŁYK, “MODEL THEORY AND PROOF THEORY OF THE GLOBAL REFLECTION PRINCIPLE”, J. symb. log., 88:2 (2023), 738  crossref
    16. LESZEK ALEKSANDER KOŁODZIEJCZYK, KATARZYNA W. KOWALIK, KEITA YOKOYAMA, “HOW STRONG IS RAMSEY'S THEOREM IF INFINITY CAN BE WEAK?”, J. symb. log., 88:2 (2023), 620  crossref
    17. David Fernández-Duque, Konstnatinos Papafilippou, Joost J. Joosten, Lecture Notes in Computer Science, 13137, Logical Foundations of Computer Science, 2022, 52  crossref
    18. ANTON FREUND, “A MATHEMATICAL COMMITMENT WITHOUT COMPUTATIONAL STRENGTH”, The Review of Symbolic Logic, 15:4 (2022), 880  crossref
    19. Stefan Hetzl, Jannik Vierling, “Unprovability results for clause set cycles”, Theoretical Computer Science, 935 (2022), 21  crossref
    20. Mateusz Łełyk, Carlo Nicolai, “A theory of implicit commitment”, Synthese, 200:4 (2022)  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Russian version PDF:660
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    References:117
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