Publications

Last update: September 28, 2011

Dissertations

  1. Beklemishev, L.D. (1992): Classification of propositional provability logics. C.Sc. (Ph.D.) Dissertation, Moscow, 104 pages. (In Russian. English translation has appeared in the volume of three selected Russian dissertations [3]).
  2. Beklemishev, L.D. (1998): Reflection principles in formal arithmetic. D.Sc. Dissertation, Moscow, 107 pages (only in Russian).  Dissertation: .ps, .pdf

Book

  1. L. Beklemishev, M. Pentus, N. Vereshchagin (1999): Provability, Complexity, Grammars, American Mathematical Society Translations, Series 2, v.192.

Volumes edited

  1. S.I. Adian, M. Baaz, L. Beklemishev, guest eds.(2005): Third Moscow-Vienna Workshop on Logic and Computation. Selected papers. Journal of Logic and Computation, Volume 15, Issue 4, August 2005.
  2. L. Beklemishev, V. Goranko, V. Shehtman, eds. (2010): Advances in Modal Logic, vol. 8, College Publications, London, UK, 2010, ix + 505 p.
  3. S. Adian, L. Beklemishev and A. Visser, guest eds. (2011): Logical Models of Reasoning and Computation. Journal of Logic and Computation, Volume 21, Issue 4, August 2011.
  4. L. Beklemishev, R. de Queiroz, eds. (2011): Logic, Language, Information, and Computation 18th International Workshop, WoLLIC 2011, Philadelphia, PA, USA, May 18-20, Proceedings. Lecture Notes in Computer Science, LNCS 6642, Springer, 2011, x+311 p.
  5. Л.Д. Беклемишев, Е.Ф. Мищенко, ред. Алгоритмические вопросы алгебры и логики, Сборник статей. К 80-летию со дня рождения академика Сергея Ивановича Адяна, Тр. МИАН, 274, МАИК, М., 2011, 351 с. (L.D. Beklemishev, E.F. Mishchenko, eds. Algorithmic aspects of algebra and logic, Collected papers. Dedicated to Academician Sergei Ivanovich Adian on the occasion of his 80th birthday, Proc. V.A. Steklov Institute of Mathematics, v. 274, Pleiades Publishing, 2011, 325 pp.)
  6. L. Beklemishev, G. Bezhanishvili, D. Mundici, Y. Venema, guest eds. Studia Logica, v. 100, No. 1-2, April 2012. Special issue dedicated to the memory of Leo Esakia.

Research papers

  1. Beklemishev, L.D. (1987): Normalization of proofs and interpolation for some logics of provability. Uspekhi Matematicheskikh Nauk, 42, 179-180 (in Russian).
  2. Beklemishev, L.D. (1989): A provability logic without Craig's interpolation property. Matematicheskie Zametki, 45, 12-22 (In Russian. English translation in Mathematical Notes, 45 (1989).)
  3. Beklemishev, L.D. (1989): On the classification of propositional provability logics. Izvestiya Akademii Nauk SSSR, ser. mat., 53, 915-943. (In Russian. English translation in Math. USSR Izvestiya, 35 (1990), 247-275.)
  4. Beklemishev, L.D. (1991): Provability logics for natural Turing progressions of arithmetical theories. Studia Logica, 50, 107-128.
  5. Beklemishev, L.D. (1992): Independent numerations of theories and recursive progressions. Sibirskii Matematichskii Zhurnal, 33, 22-46. (In Russian. English translation in Siberian Math. Journal, 33 (1992).)
  6. Beklemishev, L.D. (1993): On the complexity of arithmetical interpretations of modal formulae. Archive for Mathematical Logic, 32, 229-238.
  7. Artemov, S. and Beklemishev, L.D. (1993): On propositional quantifiers in provability logic. Notre Dame Journal of Formal Logic, 34, 401-419.
  8. Beklemishev, L.D. (1994): On bimodal logics of provability, Annals of Pure and Applied Logic, 68, 115-159.
  9. Beklemishev, L.D. (1995): On a restricted induction rule and iterated reflection principles over Kalmar elementary arithmetic. In O.B. Lupanov, editor, Theoretical and applied aspects of mathematical investigations. Moscow, Moscow State University, 1995, 36-39 (in Russian).
  10. Beklemishev, L.D. (1995): Iterated local reflection versus iterated consistency. Annals of Pure and Applied Logic, 75, 25-48.  (See also Logic Group Preprint Series  118, September 1994.)
  11. Beklemishev, L.D. (1996): Bimodal logics for extensions of arithmetical theories. The Journal of Symbolic Logic, 61, 91-124.
  12. Beklemishev L.D. (1996): Remarks on Magari algebras of PA and IΔ0+EXP. In: Logic and Algebra, P.Agliano, A.Ursini, eds., Marcel Dekker, New York, 1996, 317-325.
  13. Beklemishev, L.D. (1997): Induction rules, reflection principles, and provably recursive functions. Annals of Pure and Applied Logic, 85, 193-242.  (See also Logic Group Preprint Series  168, September 1996.)
  14. Beklemishev, L.D. (1997): Parameter free induction and reflection. In G. Gottlob, A. Leitsch, and A. Mundici, editors, Computational Logic and Proof Theory. Lecture Notes in Computer Science 1289. Springer-Verlag, Berlin, 1997, 103-113. (See also Logic Group Preprint Series  171, November 1996.)
  15. Beklemishev, L.D. (1997): Notes on local reflection principles. Theoria, 58 (3), 139-146. (See also Logic Group Preprint Series  133, May 1995.)
  16. Beklemishev, L.D. (1998): A proof-theoretic analysis of collection. Archive for Mathematical Logic, 34 (4-5), 216-238. Paper:  .ps
  17. Beklemishev, L.D. (1999): Parameter-free induction and provably total computable functions, Theoretical Computer Science 224 (1-2), 13-33, 1999. Paper:  .pdf
  18. Beklemishev, L.D. (1999): Open least element principle and bounded query computation. In J. Flum et al., editors, Computer Science Logic. CSL'99 Proceedings, Lecture Notes in Computer Science 1683, Springer-Verlag, Berlin, 389-404. Paper:  .ps
  19. Beklemishev, L.D. (2000): Another pathological well-ordering. In S. Buss et al., editors, Logic Colloquium '98 Proceedings, Lecture Notes in Logic 13, A.K.Peters, Ltd., Natick MA, 105-108. Paper:  .ps
  20. Beklemishev, L.D. (1999): Proof-theoretic analysis by iterated reflection. Paper: .ps. Archive for Mathematical Logic 42 (6), 515-552 (2003). DOI: 10.1007/s00153-002-0158-7.
  21. Beklemishev, L.D. (2003): On the induction schema for decidable predicates. The Journal of Symbolic Logic, 68 (1), p. 17-34. Preprint: Department of Philosophy, Utrecht University, Logic Group Preprint Series 205, June 2000.
  22. Rastsvetaev, A. and Beklemishev, L.D. (2002): On the query complexity of finding a local maximum point. Information Processing Letters, v. 84, p. 327-332. See also: Department of Philosophy, Utrecht University, Logic Group Preprint Series 206, November 2000.
  23. Beklemishev, L.D. (2004): Provability algebras and proof-theoretic ordinals, I. Annals of Pure and Applied Logic, v. 128, 103-124. Preprint: Department of Philosophy, Utrecht University, Logic Group Preprint Series 208, March 2001.
  24. Beklemishev, L.D. (2006): The Worm principle. In: Z. Chatzidakis, P. Koepke, W. Pohlers, editors, Logic Colloquium '02, Lecture Notes in Logic 27, ASL Publications. Preprint: Department of Philosophy, Utrecht University, Logic Group Preprint Series 219, March 2003.
  25. Beklemishev, L.D. (2003): Quantifier-free induction and the least element schema. Trudy MIAN (Proceedings of the Steklov Institute of Mathematics), v. 242, 50-67. Preliminary version in: Department of Philosophy, Utrecht University, Logic Group Preprint Series 222, April 2003.
  26. Beklemishev, L.D. and A. Visser (2004): On the limit existence principles in elementary arithmetic and related topics. Department of Philosophy, Utrecht University, Logic Group Preprint Series 224, February 2004.
  27. Beklemishev, L.D. (2005): Veblen hierarchy in the context of provability algebras. In: P. Hájek, L. Valdés-Villanueva, D. Westerståhl, eds., Logic, Methodology and Philosophy of Science, Proceedings of the Twelfth International Congress. Kings College Publications, 2005, p. 65-78. Preprint: Department of Philosophy, Utrecht University, Logic Group Preprint Series 232, June 2004.
  28. Artemov, S.N. and Beklemishev, L.D. (2004): Provability Logic. In: D.Gabbay and F.Guenthner, editors, Handbook of Philosophical Logic, 2nd ed., volume 13, pages 189-360. Springer, Dordrecht, 2004. Preliminary version: Logic Group Preprint Series 234, November 2004.
  29. Beklemishev, L.D. and A. Visser (2005): On the limit existence principles and Sigma^0_n-consequences of theories, Annals of Pure and Applied Logic, v.136, Issues 1-2 , 2005, p.56-74. Revised version of ref. [30], with an added section. .pdf.
  30. Beklemishev, L.D. and A. Visser (2005): Problems in the Logic of Provability. In: Mathematical Problems from Applied Logics. New Logics for the XXIst Century. Edited by D. Gabbay, S. Goncharov and M. Zakharyaschev. International Mathematical Series, Springer, 2005, p. 77-136. Preprint: Department of Philosophy, Utrecht University, Logic Group Preprint Series 235, May 2005.
  31. Beklemishev, L.D. (2005): Reflection principles and provability algebras in formal arithmetic. Uspehi Matematicheskih Nauk, v.60, No.2, p. 3-78. (In Russian. English translation: Russian Mathematical Surveys, v.60, No.2 (2005), 197-268.) Paper (preliminary version, in Russian):  .ps. Preprint (in English): Logic Group Preprint Series 236, May 2005.
  32. L.D. Beklemishev, J.J. Joosten, M. Vervoort (2005): A finitary treatment of the closed fragment of Japaridze's provability logic. Journal of Logic and Computation, v.15, No.4, 2005, 447-463. DOI: 10.1093/logcom/exi038, Full text. Preliminary version in: Department of Philosophy, Utrecht University, Logic Group Preprint Series 240, June 2004.
  33. Beklemishev, L.D. (2006): Representing Worms as a term rewriting system. In: Mini-Workshop "Logic, combinatorics and independence results," Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach Report No. 52/2006, p. 7-9. .pdf
  34. Beklemishev, L.D. (2007): Kripke semantics for provability logic GLP. Department of Philosophy, Utrecht University, Logic Group Preprint Series 260, November 2007.
  35. Beklemishev, L.D. (2007): On the Craig interpolation and the fixed point property for GLP. Department of Philosophy, Utrecht University, Logic Group Preprint Series 262, December 2007.
  36. L.D. Beklemishev, G. Bezhanishvili, T. Icard (2009): On topological models of GLP. Department of Philosophy, Utrecht University, Logic Group Preprint Series 278, August 2009.
  37. Beklemishev, L.D. (2010): Kripke semantics for provability logic GLP. Annals of Pure and Applied Logic, v. 161, No. 6, 2010, p. 737-744. DOI: 10.1016/j.apal.2009.06.011 Preliminary version in [43].
  38. Beklemishev L.D. (2010): Оn the Craig interpolation and the fixed point properties of GLP. In: Proofs, Categories and Computations. Essays in honor of G. Mints, S. Feferman et al. editors, "Tributes" series No. 13, College Publications, London, 2010, p. 49-60. Preliminary version in [44].
  39. L.D. Beklemishev, G. Bezhanishvili, T. Icard (2010): On topological models of GLP. In: Ways of Proof Theory, R. Schindler, ed., "Ontos Mathematical Logic" series No.2, Ontos-Verlag, Frankfurt, 2010, p. 133-153. Preliminary version in [45].
  40. Beklemishev, L.D. (2010): Ordinal completeness of bimodal provability logic GLB. Department of Philosophy, Utrecht University, Logic Group Preprint Series 282, March 2010.
  41. Л.Д. Беклемишев (2010). Теоремы Гёделя о неполноте и границы их применимости, Успехи Математических Наук, т. 65, №5, 2010, c. 61-104. .pdf. English translation: Gödel Incompleteness Theorems and the limits of their applicability, Russian Mathematical Surveys, v. 65, No.5, 2010. .pdf
  42. Beklemishev, L. and Gurevich, Y. (2011): Propositional primal logic with disjunction. Microsoft Research Technical Report, March 2011. .pdf
  43. Л.Д. Беклемишев (2011). Упрощённое доказательство теоремы об арифметической полноте для логики доказуемости GLP. Труды Математического института им. В.А. Стеклова, т. 274 (2011), с. 32-40. .pdf. English translation: A simplified proof of the arithmetical completeness theorem for the provability logic GLP. Proceedings of the Steklov Institute of Mathematics, 274(3):25–33, 2011. .pdf
  44. Beklemishev, L. and Gurevich, Y. (2014): Propositional primal logic with disjunction. Journal of Logic and Computation, v.24 (1): 257-282. published online May 2012, DOI: 10.1093/logcom/exs018 A revised version of [51].
  45. L. Beklemishev (2012): Calibrating provability logic: from modal logic to reflection calculus. In T. Bolander, T. Braüner, S. Ghilardi, L. Moss, eds. Advances in Modal Logic, v. 9, College Publications, London, 2012, pp. 89-94. .pdf
  46. L. Beklemishev, D. Gabelaia (2013). Topological completeness of the provability logic GLP. Annals of Pure and Applied Logic 164 (2013), pp. 1201-1223. DOI: 10.1016/j.apal.2013.06.008. ArXiv:1106.5693v1 [math.LO], June 2011.
  47. L. Beklemishev, D. Gabelaia (2014): Topological interpretations of provability logic. In: Leo Esakia on duality in modal and intuitionistic logics, Outstanding Contributions to Logic, 4, eds. G. Bezhanishvili, Springer, 2014, 257–290. DOI: 10.1007/978-94-017-8860-1_10. Preprint: ArXiv:1210.7317 [math.LO], October 2012.
  48. L. Beklemishev (2014): Positive provability logic for uniform reflection principles. Annals of Pure and Applied Logic, 165:1 (2014), 82–105. DOI: 10.1016/j.apal.2013.07.006. ArXiv:1304.4396 [math.LO], 2013.
  49. L. Beklemishev, D. Fernández-Duque, J. Joosten (2014): On provability logics with linearly ordered modalities. Studia Logica, 102:3 (2014), 541–566. DOI: 10.1007/s11225-013-9490-7. ArXiv:1210.4809 [math.LO], October 2012.
  50. Л. Д. Беклемишев, А. А. Оноприенко, “О некоторых медленно сходящихся системах преобразований термов”, Матем. сб., 206:9 (2015), 3–20. DOI: 10.4213/sm8519. Paper: .pdf
    English translation: L. D. Beklemishev, A. A. Onoprienko, “On some slowly terminating term rewriting systems”, Sb. Math., 206:9 (2015), 1173–1190. DOI: 10.1070/SM2015v206n09ABEH004493. Paper: .pdf
  51. L. D. Beklemishev, A note on strictly positive logics and word rewriting systems, June 2015, 8 pp., ArXiv: 1509.00666.
  52. Lev Beklemishev, Tommaso Flaminio (2016): Franco Montagna’s Work on Provability Logic and Many-valued Logic. Studia Logica, 2016, pp. 1-46. DOI: 10.1007/s11225-016-9654-3. Paper: .pdf
  53. Gerald Berger, Lev D. Beklemishev, Hans Tompits. A many-sorted variant of Japaridze's polymodal provability logic, Jan 2016, 15 pp., ArXiv: 1601.02857.
  54. Lev D. Beklemishev. Proof-theoretic analysis by iterated reflection. In: Turing's Revolution. The Impact of His Ideas about Computability. Giovanni Sommaruga and Thomas Strahm, eds., Birkhäuser, Basel, 2015, pp. 225-270. DOI: 10.1007/978-3-319-22156-4. Reprint of [29] with a new preliminary section.

Reviews

  1. Beklemishev, L.D. (1993): Review of papers by D. de Jongh, F. Montagna, and A. Carbone.
    The Journal of Symbolic Logic, 58, 715-717.
  2. Beklemishev, L.D. (1996): Review of "Diagonalization and Self-reference" by R. Smullyan.
    The Journal of Symbolic Logic, 61(3).
  3. Beklemishev, L.D. (1998): Review of "Aspects of Incompleteness" by P. Lindström.
    The Journal of Symbolic Logic, 63(4), 1606-1608. Review: .ps.pdf
  4. Beklemishev, L.D. (2001): Review of "On the arithmetical content of restricted forms of comprehension, choice and general uniform boundedness" by U. Kohlenbach. Bulletin of Symbolic Logic, 7(1), 75-77. Review: .ps , .pdf
  5. Beklemishev, L.D. (2001): Review of "Metamathematics of first-order arithmetic" by P. Hájek and P. Pudlák, to appear. Review:  .ps , .pdf
  6. Beklemishev, L.D. (2002): Review of "Fragments of Heyting arithmetic" by W. Burr. Bulletin of Symbolic Logic, 8(4), 533-534. Review:  .ps, .pdf
  7. Beklemishev, L.D. (2006): Review of "David Hilbert and the axiomatization of physics (1998–1918)" by Leo Corry, Studies In History and Philosophy of Science, Part B: Studies In History and Philosophy of Modern Physics, Volume 37, Issue 2 , June 2006, Pages 388-390. doi:10.1016/j.shpsb.2006.01.001
  8. Beklemishev, L.D. (2007): Review of "Gödel's Theorem: an incomplete guide to its use and abuse" by Torkel Franzén, Bulletin of Symbolic Logic, v. 13, No.2, 2007, pp. 241-243. Review:  .pdf

Short conference abstracts

  1. Beklemishev, L.D. (1986): Normalization of proofs and Craig's property for provability logics. Proceedings of the 8th All-Union Conference on Mathematical Logic. Moscow, September 16-18, 1986, 14 (in Russian).
  2. Beklemishev, L.D. (1987): On the cut-elimination and Craig interpolation property for provability logics. Proceedings of the VIII International LMPS Congress, Volume 1, Moscow, Nauka, 1987, 11-12.
  3. Beklemishev, L.D. (1988): Polymodal representations of Turing progressions. Proceedings of the 9th All-Union Conference on Mathematical Logic, Leningrad, Nauka, 1988, 15 (in Russian).
  4. Beklemishev, L.D. (1990): On independent numerations of arithmetical theories. Proceedings of the 10th All-Union Conference on Mathematical Logic, Alma-Ata, 1990, 14 (in Russian).
  5. Beklemishev, L.D. (1996): Fragments of arithmetic axiomatized by rules. Deutsche Mathematiker-Vereinigung, Jahrestagung 1996, Jena, 1996, 301.

Unpublished material

  1. Beklemishev, L.D. (1997): Provability and Reflection. Lecture notes for ESSLLI'97, Aix-en-Provence, preprint.
  2. Beklemishev, L.D. (2000): A note on a question of Tait:  .ps
  3. Beklemishev, L.D. (2002): Reflection principles and provability algebras. Slides of LC2002 tutorial. Münster, August 3-9, 2002. Presentation (.pdf).   Printable version: .pdf, open it in Acrobat Reader and click Ctrl-P.
  4. Beklemishev L.D. (2009): On GLP-spaces. Unpublished manuscript, January 22, 2009.   .pdf
  5. Beklemishev L.D. (2011): Provability algebras for theories of Tarskian truth. Slides of a talk at Oberwolfach seminar, November 7, 2011.   .pdf
  6. Svyatlovsky M. (2014): Positive fragments of modal logics. Course work, MIPT.   .pdf
  7. Лукашов Н. (2022): Аксиоматика геометрии оригами. Курсовая работа, факультет математики НИУ ВШЭ.   .pdf