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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Volume 274, Pages 32–40 (Mi tm3313)  
This article is cited in 11 scientific papers (total in 11 papers)

A simplified proof of arithmetical completeness theorem for provability logic GLP

L. D. Beklemishev

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (199 kB) Citations (11)
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Abstract: We present a simplified proof of Japaridze's arithmetical completeness theorem for the well-known polymodal provability logic GLP. The simplification is achieved by employing a fragment J of GLP that enjoys a more convenient Kripke-style semantics than the logic considered in the papers by Ignatiev and Boolos. In particular, this allows us to simplify the arithmetical fixed point construction and to bring it closer to the standard construction due to Solovay.
Received in November 2010
English version:
Proceedings of the Steklov Institute of Mathematics, 2011, Volume 274, Pages 25–33
DOI: https://doi.org/10.1134/S0081543811060046
Bibliographic databases:
Document Type: Article
UDC: 510.652+510.643
Language: Russian
Citation: L. D. Beklemishev, “A simplified proof of arithmetical completeness theorem for provability logic GLP”, Algorithmic aspects of algebra and logic, Collected papers. Dedicated to Academician Sergei Ivanovich Adian on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 274, MAIK Nauka/Interperiodica, Moscow, 2011, 32–40; Proc. Steklov Inst. Math., 274 (2011), 25–33
Citation in format AMSBIB
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\by L.~D.~Beklemishev
\paper A simplified proof of arithmetical completeness theorem for provability logic $\mathbf{GLP}$
\inbook Algorithmic aspects of algebra and logic
\bookinfo Collected papers. Dedicated to Academician Sergei Ivanovich Adian on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2011
\vol 274
\pages 32--40
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • https://www.mathnet.ru/eng/tm/v274/p32
    • This publication is cited in the following 11 articles:
    1. Izv. Math., 89:1 (2025), 1–14  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    2. Bagaria J., “Derived Topologies on Ordinals and Stationary Reflection”, Trans. Am. Math. Soc., 371:3 (2019), 1981–2002  crossref  mathscinet  zmath  isi  scopus
    3. Fernandez-Duque D., Joosten J.J., “The Omega-Rule Interpretation of Transfinite Provability Logic”, Ann. Pure Appl. Log., 169:4 (2018), 333–371  crossref  mathscinet  zmath  isi
    4. Berger G., Beklemishev L.D., Tompits H., “A Many-Sorted Variant of Japaridze'S Polymodal Provability Logic”, Log. J. IGPL, 26:5 (2018), 505–538  crossref  mathscinet  isi  scopus
    5. Beklemishev L.D., “On the Reduction Property For Glp-Algebras”, Dokl. Math., 95:1 (2017), 50–54  mathnet  crossref  mathscinet  zmath  isi
    6. F. N. Pakhomov, “Linear GLP-algebras and their elementary theories”, Izv. Math., 80:6 (2016), 1159–1199  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Shamkanov D., “Nested Sequents For Provability Logic Glp”, Log. J. IGPL, 23:5 (2015), 789–815  crossref  mathscinet  isi  scopus
    8. Beklemishev L., “Positive Provability Logic for Uniform Reflection Principles”, Ann. Pure Appl. Log., 165:1, SI (2014), 82–105  crossref  mathscinet  zmath  isi  elib
    9. Beklemishev L.D., Fernandez-Duque D., Joosten J.J., “On Provability Logics with Linearly Ordered Modalities”, Stud. Log., 102:3 (2014), 541–566  crossref  mathscinet  zmath  isi  elib
    10. Lev Beklemishev, David Gabelaia, Outstanding Contributions to Logic, 4, Leo Esakia on Duality in Modal and Intuitionistic Logics, 2014, 257  crossref
    11. Daniyar S. Shamkanov, “Interpolation properties for provability logics GL and GLP”, Proc. Steklov Inst. Math., 274 (2011), 303–316  mathnet  crossref  mathscinet  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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