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Beklemishev, Lev Dmitrievich

Total publications: 91 (69)
in MathSciNet: 67 (56)
in zbMATH: 54 (46)
in Web of Science: 50 (40)
in Scopus: 49 (41)
Cited articles: 48
Citations in Math-Net.Ru: 59
Citations in MathSciNet: 322
Citations in Web of Science: 343
Citations in Scopus: 426
Presentations: 72

Number of views:
This page:11252
Abstract pages:7894
Full texts:2533
References:500
Beklemishev, Lev Dmitrievich
Member of the Russian Academy of Sciences
Doctor of physico-mathematical sciences (1998)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
Birth date: 17.09.1967
Phone: +7 (495) 984 81 43
Fax: +7 (499) 135 05 55
E-mail: ,
Website: http://www.mi.ras.ru/~bekl
Keywords: mathematical logic, proof theory, provability logic, modal logic, fragments of arithmetic.
UDC: 510.2, 510.23, 510.58, 510.6, 510.643, 510.65, 510.652, 512
MSC: 03F45, 03F03, 03F40, 03F15, 03F20, 03F30, 03B45, 03B70

Subject:

Classification theorem for propositional provability logics is proved. A characterization of restricted induction rules in arithmetic in terms of iterated reflection principles is obtained. Classes of provably total computable functions for fragments of arithmetic with parameter-free induction are characterized. In particular, parameter-free induction for Π2-formulas corresponds to the class of primitive recursive functions. An approach to the theory of proof-theoretic ordinals on the basis of a notion of provability algebra is suggested.

Biography

Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonossov Moscow State University in 1989 (department of Mathematical Logic); 1989–1992 — a Ph.D. student; since 1992 — staff member of V. A. Steklov Mathematical Institute of Russian Academy of Sciences. Ph.D. thesis was defended in 1992. Title: Classification of propositional provability logics. D.Sci. thesis was defended in 1998. Title: Reflection principles in formal arithmetic.
In 2000–2005 L. Beklemishev was a faculty member of Utrecht University (the Netherlands).
Moscow Mathematical Society prize was awarded in 1994 for the paper "On the classification of propositional provability logics". A. von Humboldt Fellowship (Germany) was awarded in 1998. In 2006 L. Beklemishev was elected a corresponding member of Russian Academy of Sciences.

   
Main publications:
  1. L. D. Beklemishev, “On the classification of propositional provability logics”, Izv. Akad. Nauk SSSR Ser. Mat., 53:5 (1989), 915–943  mathnet  mathscinet  zmath; English transl. Math. USSR-Izv., 35:2 (1990), 247–275  crossref  mathscinet  zmath
  2. L. D. Beklemishev, “Iterated local reflection versus iterated consistency”, Ann. Pure Appl. Logic, 75 (1995), 25–48  crossref  mathscinet  zmath
  3. L. D. Beklemishev, “A proof-theoretic analysis of collection”, Arch. Math. Logic, 37:5-6 (1998), 275–296  crossref  mathscinet  zmath
  4. L. D. Beklemishev, “Parameter-free induction and provably total computable functions”, Theoret. Comput. Sci., 224 (1999), 13–33  crossref  mathscinet  zmath
  5. L. D. Beklemishev, “Reflection principles and provability algebras in formal arithmetic”, Uspekhi Matematicheskikh Nauk, 60:2 (2005), 3–78  mathnet  mathscinet  zmath; English transl. Russian Mathematical Surveys, 60:2 (2005), 197–268  crossref  mathscinet  zmath

http://www.mathnet.ru/eng/person17809
http://scholar.google.com/citations?user=QUJVc2UAAAAJ&hl=en
http://zbmath.org/authors/?q=ai:beklemishev.lev-d
https://mathscinet.ams.org/mathscinet/MRAuthorID/251033
http://elibrary.ru/author_items.asp?authorid=7524
ISTINA http://istina.msu.ru/workers/2556926
http://orcid.org/0000-0002-2949-0600
http://www.researcherid.com/rid/F-7814-2013
http://www.scopus.com/authid/detail.url?authorId=6602096489
https://www.researchgate.net/profile/Lev_Beklemishev

Full list of publications:
| by years | by types | by times cited in WoS | by times cited in Scopus | scientific publications | common list |



   2020
1. L. D. Beklemishev, A. V. Vasil'ev, E. P. Vdovin, S. S. Goncharov, V. V. Kozlov, P. S. Kolesnikov, V. D. Mazurov, Yu. V. Matiyasevich, A. S. Morozov, A. N. Parshin, V. G. Puzarenko, M. V. Schwidefsky, “Yurii Leonidovich Ershov (on his 80th birthday)”, Uspekhi Mat. Nauk, 75:3(453) (2020), 191–194  mathnet  crossref

   2019
2. Lev D. Beklemishev, Fedor N. Pakhomov, Reflection algebras and conservation results for theories of iterated truth, 2019 , 48 pp., arXiv: 1908.10302
3. E. A. Kolmakov, L. D. Beklemishev, “Axiomatization of provable $n$-provability”, J. Symb. Log., 84:2 (2019), 849–869  mathnet  crossref  mathscinet  isi (cited: 1)  scopus (cited: 1)
4. S. I. Adian, N. N. Andreev, L. D. Beklemishev, S. S. Goncharov, Yu. L. Ershov, Yu. V. Matiyasevich, Yu. S. Osipov, M. R. Pentus, V. A. Plungyan, E. V. Rakhilina, V. A. Sadovnichii, A. L. Semenov, S. G. Tatevosov, V. M. Tikhomirov, A. Kh. Shen, “Vladimir Andreevich Uspensky (27/11/1930–27/6/2018)”, Russian Math. Surveys, 74:4 (2019), 735–753  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
5. V. A. Alexandrov, L. D. Beklemishev, V. M. Buchstaber, A. Yu. Vesnin, A. A. Gaifullin, N. P. Dolbilin, N. Yu. Erokhovets, M. D. Kovalev, V. S. Makarov, S. P. Novikov, D. O. Orlov, A. N. Parshin, I. Kh. Sabitov, D. V. Treschev, O. K. Sheinman, E. V. Shchepin, “Mikhail Ivanovich Shtogrin (on his 80th birthday)”, Russian Math. Surveys, 74:6 (2019), 1159–1162  mathnet  crossref  crossref  mathscinet  adsnasa  isi
6. L. D. Beklemishev, “Matematika i logika”, Matematicheskaya sostavlyayuschaya, 2-e izd., rassh. i dop., eds. N. N. Andreev, S. P. Konovalov, N. M. Panyunin, Matematicheskie etyudy, M., 2019, 242 https://book.etudes.ru/toc/mathnlogic/

   2018
7. Lev Beklemishev, “A note on strictly positive logics and word rewriting systems”, Larisa Maximova on Implication, Interpolation, and Definability, Outst. Contrib. Log., 15, eds. Sergei Odintsov, Springer, Berlin, Heidelberg, 2018, 61–70  mathnet  crossref  mathscinet  isi (cited: 3)  scopus (cited: 5)
8. L. D. Beklemishev, “Reflection calculus and conservativity spectra”, Russian Math. Surveys, 73:4 (2018), 569–613  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus (cited: 1)
9. Lev D. Beklemishev, “A universal algebra for the variable-free fragment of $RC^\nabla$”, Logical Foundations of Computer Science, International Symposium, LFCS 2018, Lecture Notes in Comput. Sci., 10703, Springer, Berlin, Heidelberg, 2018, 91–106  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 3)
10. Gerald Berger, L. D. Beklemishev, Hans Tompits, “A many-sorted variant of Japaridze's polymodal provability logic”, Log. J. IGPL, 26:5 (2018), 505–538  mathnet  crossref  mathscinet  isi  scopus
11. L. D. Beklemishev, A universal Kripke frame for the variable-free fragment of RC∇, 2018 , 5 pp., arXiv: 1804.02641
12. E. A. Kolmakov, L. D. Beklemishev, “Axiomatizing provable $n$-provability”, Dokl. Math., 98:3 (2018), 582–585  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus

   2017
13. Lev D. Beklemishev, Reflection calculus and conservativity spectra, 2017 , 28 pp., arXiv: 1703.09314
14. L. D. Beklemishev, “On the Reduction Property for GLP-Algebras”, Dokl. Math., 95:1 (2017), 50–54  mathnet  crossref  crossref  mathscinet  isi (cited: 3)  elib  scopus (cited: 3)
15. Lev D. Beklemishev, “On the reflection calculus with partial conservativity operators”, Lecture Notes in Comput. Sci., 10388, 2017, 48–67  mathnet  crossref  mathscinet  zmath  isi (cited: 5)  scopus (cited: 6)
16. Lev Beklemishev, “Guest Editorial: Computer Science Symposium in Russia”, Theory Comput. Syst., 61:2 (2017), 462–463 https://link.springer.com/content/pdf/10.1007  crossref  mathscinet  zmath  isi  scopus

   2016
17. L. D. Beklemishev, “Proof theoretic analysis by iterated reflection”, Turing's revolution, Part II, Birkhäuser/Springer, Cham, 2016, 225–270  crossref  mathscinet  scopus (cited: 1)
18. Lev Beklemishev, Tommaso Flaminio, “Franco Montagna's work on provability logic and many-valued logic”, Studia Logica, 104:1 (2016), 1–46  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
19. L. D. Beklemishev, Notes on a reduction property for GLP-algebras, 2016 , 8 pp., arXiv: 1606.00290
20. Lev Beklemishev, Daniyar Shamkanov, “Some abstract versions of Gödel's second incompleteness theorem based on non-classical logics”, Liber Amicorum Alberti: A tribute to Albert Visser, Tributes, 30, eds. Jan van Eijck, Rosalie Iemhoff and Joost J. Joosten, College Publications, London, 2016, 15–29 url, arXiv: 1602.05728  mathscinet  zmath
21. Gerald Berger, Lev D. Beklemishev, Hans Tompits, A Many-Sorted Variant of Japaridze's Polymodal Provability Logic, 2016 , 15 pp., arXiv: 1601.02857
22. Lev Beklemishev, “Notes on a reduction property of GLP-algebras”, 11th International Conference on Advances in Modal Logic, Short Papers (Budapest, 30 August – 2 September, 2016), 2016, 7–13
23. Advances in Modal Logic, v. 11, eds. Lev Beklemishev, Stephane Demri, Andras Mate, College Publications, London, 2016 , xii+570 pp.  mathscinet  zmath

   2015
24. L. D. Beklemishev, A note on strictly positive logics and word rewriting systems, 2015 , 8 pp., arXiv: 1509.00666
25. L. D. Beklemishev, A. A. Onoprienko, “On some slowly terminating term rewriting systems”, Sb. Math., 206:9 (2015), 1173–1190  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 4)  elib  elib  scopus (cited: 4)
26. L. D. Beklemishev, D. V. Musatov (eds.), Computer Science – Theory and Applications, 10th International Computer Science Symposium in Russia, CSR 2015, Listvyanka, Russia, July 13–17, 2015, Proceedings, Lecture Notes in Computer Science, 9139, Springer, 2015 , xx+443 pp.  crossref  mathscinet  zmath  scopus

   2014
27. L. D. Beklemishev, D. Fernández-Duque, J. J. Joosten, “On provability logics with linearly ordered modalities”, Studia Logica, 102:3 (2014), 541–566 , arXiv: 1210.4809  mathnet  crossref  mathscinet  zmath  isi (cited: 9)  elib (cited: 1)  scopus
28. L. Beklemishev, “Positive provability logic for uniform reflection principles”, Ann. Pure Appl. Logic, 165:1 (2014), 82–105  mathnet  crossref  mathscinet  zmath  isi (cited: 10)  elib  scopus (cited: 14)
29. L. Beklemishev, Y. Gurevich, “Propositional primal logic with disjunction”, J. Logic Comput., 24:1 (2014), 257–282  mathnet  crossref  mathscinet  zmath  isi (cited: 8)  elib (cited: 5)  scopus (cited: 12)
30. L. Beklemishev, D. Gabelaia, “Topological interpretations of provability logic”, Leo Esakia on duality in modal and intuitionistic logics, Outstanding Contributions to Logic, 4, eds. G. Bezhanishvili, Springer, 2014, 257–290 , arXiv: 1210.7317  crossref  mathscinet  zmath  scopus (cited: 6)
31. Lev Beklemishev, Ruy De Queiroz, Andre Scedrov, “Editors' foreword”, Journal of Computer and System Sciences, 80:6, Special Issue: 18th Workshop on Logic, Language, Information and Computation (WoLLIC 2011) (2014), 1037  crossref  mathscinet  zmath  isi

   2013
32. L. Beklemishev, D. Gabelaia, “Topological completeness of the provability logic GLP”, Ann. Pure Appl. Logic, 164:12 (2013), 1201–1223 , arXiv: 1106.5693  mathnet  crossref  mathscinet  zmath  isi (cited: 11)  elib (cited: 4)  scopus (cited: 13)
33. L. D. Beklemishev, “Pozitivnye logiki dokazuemosti”, Mezhdunarodnaya konferentsiya “Maltsevskie chteniya”. Tezisy dokladov (Novosibirsk, 11–15 noyabrya 2013 g.), FGBUN Institut matematiki im. S.L. Soboleva SO RAN; Novosibirskii gosudarstvennyi universitet, Novosibirsk, 2013, 10 www.math.nsc.ru/conference/malmeet/13/maltsev13.pdf

   2012
34. L. D. Beklemishev, “Calibrating provability logic: from modal logic to reflection calculus”, Advances in Modal Logic, 9, eds. T. Bolander, T. Braüner, S. Ghilardi, L. Moss, College Publications, London, 2012, 89–94  mathscinet  zmath  elib
35. L. Beklemishev, “DKAL: A Distributed Knowledge Authorization Language and Its Logic of Information”, Computer Science – Theory and Applications. 7th International Computer Science Symposium in Russia, CSR 2012 (Nizhny Novgorod, Russia, July 3–7, 2012), Lecture Notes in Computer Science, 7353, eds. E. Hirsch, J. Karhumäki, A. Lepistö, M. Prilutskii, Springer, 2012, XIII–XIV  crossref  mathscinet
36. L. Beklemishev, G. Bezhanishvili, D. Mundici, Y. Venema, “Foreword [Special issue dedicated to the memory of Leo Esakia]”, Studia Logica, 100:1-2 (2012), 1–7  crossref  mathscinet  zmath  isi  scopus

   2011
37. L. Beklemishev, Y. Gurevich, Propositional primal logic with disjunction, Microsoft Research Technical Report MSR-TR-2011-35, Redmond, 2011 , 31 pp. http://research.microsoft.com/apps/pubs/default.aspx?id=146631
38. L. D. Beklemishev, “A simplified proof of arithmetical completeness theorem for provability logic GLP”, Proc. Steklov Inst. Math., 274:1 (2011), 25–33  mathnet  crossref  mathscinet  zmath  isi (cited: 9)  elib (cited: 3)  elib (cited: 3)  scopus (cited: 6)
39. L. Beklemishev, “Ordinal completeness of bimodal provability logic GLB”, Logic, language, and computation, 8th International Tbilisi Symposium TbiLLC 2009, Lecture Notes in Comput. Sci., 6618, eds. N. Bezhanishvili et al., Springer, Heidelberg, 2011, 1–15  crossref  mathscinet  zmath  isi (cited: 5)  scopus (cited: 5)
40. L. D. Beklemishev, V. M. Buchstaber, I. G. Lysenok, A. A. Mal'tsev, S. P. Novikov, A. A. Razborov, A. L. Semenov, “Sergei Ivanovich Adian (on his eightieth birthday)”, Russian Math. Surveys, 66:1 (2011), 197–198  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
41. L. Beklemishev, R. de Queiroz (eds.), Logic, language, information, and computation, 18th International Workshop, WoLLIC 2011 (Philadelphia, PA, USA, May 18–20, 2011), Proceedings, Lecture Notes in Comput. Sci., 6642, Springer, 2011 , x+311 pp.  crossref  zmath
42. Algoritmicheskie voprosy algebry i logiki, Sbornik statei. K 80-letiyu so dnya rozhdeniya akademika Sergeya Ivanovicha Adyana, Tr. MIAN, 274, ed. L. D. Beklemishev, E. F. Mischenko, MAIK «Nauka/Interperiodika», M., 2011 , 351 pp.  mathnet
43. L. D. Beklemishev, “Foreword”, Proc. Steklov Inst. Math., 274 (2011), 1–3  mathnet  crossref  mathscinet  elib  scopus (cited: 13)  scopus (cited: 13)
44. S. Adian, L. Beklemishev, A. Visser, “Proof and Computation”, J. Logic Computation, 21:4 (2011), 541–542  crossref  mathscinet  isi  scopus

   2010
45. L. D. Beklemishev, “Gödel incompleteness theorems and the limits of their applicability. I”, Russian Math. Surveys, 65:5 (2010), 857–899  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 2)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 3)
46. L. D. Beklemishev, “Kripke semantics for provability logic GLP”, Ann. Pure Appl. Logic, 161:6 (2010), 756–774  crossref  mathscinet  zmath  isi (cited: 15)  elib (cited: 11)  scopus (cited: 18)
47. L. Beklemishev, V. Goranko, V. Shehtman (eds.), Advances in Modal Logic, 8, College Publications, London, 2010 , ix+505 pp.  mathscinet
48. L. Beklemishev, G. Bezhanishvili, T. Icard, “On topological models of GLP”, Ways of proof theory, Ontos Mathematical Logic, 2, eds. R. Schindler, Ontos Verlag, Frankfurt, 2010, 133–153  mathscinet
49. L. Beklemishev, “On the Craig interpolation and the fixed point properties of GLP”, Proofs, categories and computations, Tributes, 13, eds. S. Feferman et al., College Publications, London, 2010, 49–60  mathscinet  zmath

   2007
50. L. Beklemishev, “Review of “Gödel's Theorem: an incomplete guide to its use and abuse” by Torkel Franzén”, Bulletin of Symbolic Logic, 13:2 (2007), 241–243  crossref

   2006
51. L. D. Beklemishev, “The Worm principle”, Logic Colloquium '02 (Münster, 2002), Lect. Notes Log., 27, Assoc. Symbol. Logic, La Jolla, CA, 2006, 75–95  mathscinet  zmath  isi (cited: 13)
52. L. Beklemishev, A. Visser, “Problems in the logic of provability”, Mathematical problems from applied logic. I, Int. Math. Ser. (N. Y.), 4, Springer, New York, NY, 2006, 77–136  crossref  mathscinet  zmath
53. L. Beklemishev, “Representing Worms as a term rewriting system”, Logic, combinatorics and independence results, Oberwolfach Report, 52/2006, eds. A. Bovykin, L. Carlucci, A. Weiermann, Mathematisches Forschungsinstitut Oberwolfach, 2006, 7–9  mathscinet
54. L. D. Beklemishev, I. G. Lysenok, A. A. Mal'tsev, S. P. Novikov, M. R. Pentus, A. A. Razborov, A. L. Semenov, V. A. Uspenskii, “Sergei Ivanovich Adian (on his 75th birthday)”, Russian Math. Surveys, 61:3 (2006), 575–588  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
55. L. Beklemishev, “Review of “David Hilbert and the axiomatization of physics (1898–-1918)” by Leo Corry”, Studies In History and Philosophy of Science, Part B: Studies In History and Philosophy of Modern Physics, 37:2 (2006), 388–390  crossref  mathscinet  isi

   2005
56. L. D. Beklemishev, A. Visser, “On the limit existence principles in elementary arithmetic and $\Sigma^0_n$-consequences of theories”, Ann. Pure Appl. Logic, 136:1-2 (2005), 56–74  crossref  mathscinet  zmath  isi (cited: 10)  elib (cited: 5)  scopus (cited: 9)
57. L. D. Beklemishev, J. J. Joosten, M. Vervoort, “A finitary treatment of the closed fragment of Japaridze's provability logic”, J. Logic Comput., 15:4 (2005), 447–463  crossref  mathscinet  zmath  isi (cited: 16)  elib (cited: 3)  scopus (cited: 19)
58. L. D. Beklemishev, “Reflection principles and provability algebras in formal arithmetic”, Russian Math. Surveys, 60:2 (2005), 197–268  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 35)  elib (cited: 21)  elib (cited: 21)  scopus (cited: 40)
59. S. I. Adian, M. Baaz, L. D. Beklemishev, “Editorial”, J. Logic Computation, 15:4 (2005), 409  crossref  mathscinet  isi  scopus

   2004
60. L. D. Beklemishev, “Provability algebras and proof-theoretic ordinals. I”, Ann. Pure Appl. Logic, 128:1-3 (2004), 103–123  crossref  mathscinet  zmath  isi (cited: 41)  elib (cited: 28)  scopus (cited: 49)

   2003
61. L. D. Beklemishev, “Proof-theoretic analysis by iterated reflection”, Arch. Math. Logic, 42:6 (2003), 515–552  crossref  mathscinet  zmath  isi (cited: 30)  elib (cited: 16)  scopus (cited: 32)
62. L. D. Beklemishev, “On the induction schema for decidable predicates”, J. Symbolic Logic, 68:1 (2003), 17–34  crossref  mathscinet  zmath  isi (cited: 8)  elib (cited: 6)  scopus (cited: 7)
63. L. D. Beklemishev, “Quantifier-Free Induction Schema and the Least Element Principle”, Proc. Steklov Inst. Math., 242 (2003), 50–66  mathnet  mathscinet  zmath

   2002
64. A. L. Rastsvetaev, L. D. Beklemishev, “On the query complexity of finding a local maximum point”, Inform. Process. Lett., 84:6 (2002), 327–332  crossref  mathscinet  zmath  isi (cited: 2)  elib  scopus (cited: 2)

   2001
65. L. Beklemishev, “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 (2001), 75–77  crossref

   2000
66. L. Beklemishev, “Another pathological well-ordering”, Logic Colloquium '98 (Prague, 1998), Lect. Notes Log., 13, Assoc. Symbol. Logic, Urbana, IL, 2000, 105–108  crossref  mathscinet  zmath  isi

   1999
67. L. D. Beklemishev, “Open least element principle and bounded query computation”, Computer science logic (Madrid, 1999), Lecture Notes in Comput. Sci., 1683, Springer, Berlin, 1999, 389–404  crossref  mathscinet  zmath  isi (cited: 3)  elib
68. L. D. Beklemishev, “Classification of propositional provability logics”, Provability, complexity, grammars, Amer. Math. Soc. Transl. Ser. 2, 192, Amer. Math. Soc., Providence, RI, 1999, 1–56  mathscinet  zmath
69. L. Beklemishev, M. Pentus, N. Vereshchagin, Provability, complexity, grammars, Amer. Math. Soc. Transl. Ser. 2, 192, Amer. Math. Soc., Providence, RI, 1999 , x+172 pp.  mathscinet  zmath
70. L. D. Beklemishev, “Parameter free induction and provably total computable functions”, Theoret. Comput. Sci., 224:1-2 (1999), 13–33  crossref  mathscinet  zmath  isi (cited: 16)  elib (cited: 13)  scopus (cited: 20)

   1998
71. L. D. Beklemishev, “A proof-theoretic analysis of collection”, Arch. Math. Logic, 37:5-6 (1998), 275–296  crossref  mathscinet  zmath  isi (cited: 20)  elib (cited: 18)  scopus (cited: 22)
72. L. D. Beklemishev, Skhemy refleksii v formalnoi arifmetike, Diss. … dokt. fiz.-matem. nauk, Matematicheskii institut im. V.A. Steklova, Moskva, 1998 , 149 pp.
73. L. Beklemishev, “Review of “Aspects of Incompleteness” by P. Lindström”, The Journal of Symbolic Logic, 63:4 (1998), 1606–1608  crossref

   1997
74. L. Beklemishev, “Notes on local reflection principles”, Theoria, 63:3 (1997), 139–146  crossref  mathscinet  scopus (cited: 8)
75. L. D. Beklemishev, “Parameter free induction and reflection”, Computational logic and proof theory (Vienna, 1997), Lecture Notes in Comput. Sci., 1289, Springer, Berlin, 1997, 103–113  crossref  mathscinet  zmath
76. L. D. Beklemishev, “Induction rules, reflection principles, and provably recursive functions”, Ann. Pure Appl. Logic, 85:3 (1997), 193–242  crossref  mathscinet  zmath  isi (cited: 30)  elib (cited: 28)  scopus (cited: 33)

   1996
77. L. Beklemishev, “Remarks on Magari algebras of $\mathrm{PA}$ and $\mathrm{I}\Delta_0+\mathrm{EXP}$”, Logic and algebra (Pontignano, 1994), Lecture Notes in Pure and Appl. Math., 180, Marcel Dekker, New York, 1996, 317–325  mathscinet  zmath  isi (cited: 3)
78. L. D. Beklemishev, “Bimodal logics for extensions of arithmetical theories”, J. Symbolic Logic, 61:1 (1996), 91–124  crossref  mathscinet  zmath  isi (cited: 3)  elib (cited: 7)  scopus (cited: 7)
79. L. Beklemishev, “Review of “Diagonalization and Self-reference” by R. Smullyan”, The Journal of Symbolic Logic, 61:3 (1996), 1052–1055  crossref

   1995
80. L. Beklemishev, “Iterated local reflection versus iterated consistency”, Ann. Pure Appl. Logic, 75:1-2 (1995), 25–48  crossref  mathscinet  zmath  isi (cited: 15)  elib (cited: 5)  scopus (cited: 16)
81. L. D. Beklemishev, “Ob ogranichennom pravile induktsii i iterirovannykh skhemakh refleksii nad kalmarovskoi elementarnoi arifmetikoi”, Teoreticheskie i prikladnye aspekty matematicheskikh issledovanii, eds. O. B. Lupanov, MGU, Moskva, 1995, 36–39

   1994
82. L. D. Beklemishev, “On bimodal logics of provability”, Ann. Pure Appl. Logic, 68:2 (1994), 115–159  crossref  mathscinet  zmath  isi (cited: 6)  elib (cited: 4)  scopus (cited: 8)

   1993
83. S. N. Artemov, L. D. Beklemishev, “On propositional quantifiers in provability logic”, Notre Dame J. Formal Logic, 34:3 (1993), 401–419  crossref  mathscinet  zmath  scopus (cited: 10)
84. L. D. Beklemishev, “On the complexity of arithmetical interpretations of modal formulae”, Arch. Math. Logic, 32:3 (1993), 229–238  crossref  mathscinet  zmath  isi (cited: 4)  elib (cited: 1)  scopus (cited: 5)
85. L. Beklemishev, “Review of papers by D. de Jongh, F. Montagna, and A. Carbone”, The Journal of Symbolic Logic, 58 (1993), 715–717  scopus (cited: 5)

   1992
86. L. D. Beklemishev, “Independent enumerations of theories and recursive progressions”, Siberian Math. J., 33:5 (1992), 760–783  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 2)
87. L. D. Beklemishev, Klassifikatsiya propozitsionalnykh logik dokazuemosti, Diss. … kand. fiz.-matem. nauk, Matematicheskii institut im. V.A. Steklova RAN, Moskva, 1992

   1991
88. L. D. Beklemishev, “Provability logics for natural Turing progressions of arithmetical theories”, Studia Logica, 50:1 (1991), 107–128  crossref  mathscinet  elib (cited: 2)  scopus (cited: 9)

   1990
89. L. D. Beklemishev, “On the classification of propositional provability logics”, Math. USSR-Izv., 35:2 (1990), 247–275  mathnet  crossref  mathscinet  zmath  isi  scopus (cited: 4)

   1989
90. L. D. Beklemishev, “Provability logic without Craig's interpolation property”, Math. Notes, 45:6 (1989), 437–450  mathnet  crossref  mathscinet  zmath  isi  scopus

   1987
91. L. D. Beklemishev, “Normalization of deductions and interpolation for some logics of provability”, Russian Math. Surveys, 42:6 (1987), 223–224  mathnet  crossref  mathscinet  zmath  adsnasa  isi  scopus

Presentations in Math-Net.Ru
1. Introductory words
L. D. Beklemishev
S. I. Adian memorial conference
May 26, 2020 14:55
2. Lecture 21. Applications of functional interpretation. Interpretation by absence of counterexample. T system models
L. D. Beklemishev
L. D. Beklemishev, S. L. Kuznetsov. Computational proof theory and lambda calculus
May 12, 2020 16:30   
3. Лекция 20. Гёделевская система Т. Интерпретация формальной арифметики в Т (продолжение)
L. D. Beklemishev
L. D. Beklemishev, S. L. Kuznetsov. Computational proof theory and lambda calculus
April 28, 2020 16:30   
4. Лекция 19. Гёделевская система $Т$. Функциональная интерпретация интуиционистской арифметики в $Т$
L. D. Beklemishev
L. D. Beklemishev, S. L. Kuznetsov. Computational proof theory and lambda calculus
April 21, 2020   
5. Лекция 18. Интуиционистская арифметика
L. D. Beklemishev
L. D. Beklemishev, S. L. Kuznetsov. Computational proof theory and lambda calculus
April 14, 2020 16:30   
6. Лекция 17. Примитивно рекурсивная арифметика
L. D. Beklemishev
L. D. Beklemishev, S. L. Kuznetsov. Computational proof theory and lambda calculus
April 7, 2020   
7. Лекция 16. Негативная интерпретация классической логики в интуиционистской
L. D. Beklemishev
L. D. Beklemishev, S. L. Kuznetsov. Computational proof theory and lambda calculus
March 26, 2020 16:00   
8. Лекция 15. Интуиционистское исчисление предикатов. Гильбертовский и генценовский формат. Теорема об устранении сечения. Дизъюнктивное и экзистенциальное свойства интуиционистской логики.
L. D. Beklemishev
L. D. Beklemishev, S. L. Kuznetsov. Computational proof theory and lambda calculus
March 23, 2020 16:30   
9. Лекция 13. Слабо экстенсиональные лямбда-алгебры. Модель Плоткина $\mathcal{P}\omega$.
L. D. Beklemishev
L. D. Beklemishev, S. L. Kuznetsov. Computational proof theory and lambda calculus
March 2, 2020 16:30   
10. Лекция 12. Комбинаторные алгебры, лямбда-алгебры.
L. D. Beklemishev
L. D. Beklemishev, S. L. Kuznetsov. Computational proof theory and lambda calculus
February 17, 2020 16:30   
11. Лекция 11. Модели лямбда-исчисления
L. D. Beklemishev, S. L. Kuznetsov
L. D. Beklemishev, S. L. Kuznetsov. Computational proof theory and lambda calculus
February 10, 2020 16:30   
12. Лекция 10. Комбинаторная логика
L. D. Beklemishev
L. D. Beklemishev, S. L. Kuznetsov. Computational proof theory and lambda calculus
December 9, 2019 16:30   
13. Об открытых вопросах теории доказательств
L. D. Beklemishev
Seminars "Proof Theory" and "Logic Online Seminar"
October 14, 2019
14. Лекция 1.Введение. Бестиповое лямбда-исчисление. Представление натуральных чисел в бестиповом лямбда-исчислении
L. D. Beklemishev, S. L. Kuznetsov
L. D. Beklemishev, S. L. Kuznetsov. Computational proof theory and lambda calculus
September 30, 2019   
15. Итерированные определения истинности и исчисление рефлексий
L. D. Beklemishev
Seminars "Proof Theory" and "Logic Online Seminar"
April 29, 2019 18:30   
16. Лекция 16. Соотношение между принципом Червя и доказуемо-вычислимыми функциями PA.
L. D. Beklemishev

March 4, 2019 16:30   
17. Лекция 15. Теоретико-доказательственный анализ $\mathsf{PA}$ с помощью схем рефлексии.
L. D. Beklemishev

February 25, 2019 16:30   
18. Ordinals and conservativity spectra of arithmetical theories
L. D. Beklemishev
Steklov Mathematical Institute Seminar
February 21, 2019 16:00   
19. Лекция 14. Лемма о редукции для схем рефлексии.
L. D. Beklemishev

February 18, 2019 16:30   
20. Лекция 13. Доказуемо вычислимые функции $\mathsf{PA}$, принцип Червя, схемы рефлексии.
L. D. Beklemishev

February 11, 2019 16:30   
21. Лекция 9. Иерархия Веблена.
L. D. Beklemishev

November 26, 2018 16:30   
22. Исчисление для схем рефлексии и спектры консервативности
L. D. Beklemishev
Scientific session of the Steklov Mathematical Institute of RAS dedicated to the results of 2018
November 21, 2018 14:00   
23. Лекция 8. Ординалы. Канторовская система ординальных обозначений для ординала $\varepsilon_0$.
L. D. Beklemishev

November 19, 2018 16:30   
24. Лекция 7. Теорема Парсонса-Минца-Такеути о доказуемо вычислимых функциях $\mathsf{I}\Sigma_1$ (Часть 2).
F. N. Pakhomov, L. D. Beklemishev

November 12, 2018 16:30   
25. О спектрах консервативности арифметических теорий
L. D. Beklemishev
Seminar of the Department of Mathematical Logic "Algorithmic problems in algebra and logic"
November 6, 2018 18:30
26. Как теория доказательств пришла к своим ординалам
L. D. Beklemishev
MIPT Interdepartmental Seminar on Discrete Mathematics
October 17, 2018 18:30
27. Лекция 4. Исчисление секвенций в формате Тейта и теорема о полноте для него.
L. D. Beklemishev, F. N. Pakhomov

October 15, 2018 16:30   
28. Лекция 3. Доказуемо вычислимые функции теории $\mathsf{EA}$.
L. D. Beklemishev

October 8, 2018 16:30   
29. Лекция 2. Арифметка элементарных функций $\mathsf{EA}$.
L. D. Beklemishev

October 1, 2018 16:30   
30. Лекция 1. Программа Гильберта и основания математики. Элементарные по Кальмару функции.
L. D. Beklemishev

September 24, 2018 16:30   
31. Доказуемо рекурсивные функции, занятие 4
L. D. Beklemishev
Summer School "Contemporary Mathematics" named Vitaly Arnold, 2018
July 25, 2018 11:15   
32. Доказуемо рекурсивные функции, занятие 3
L. D. Beklemishev
Summer School "Contemporary Mathematics" named Vitaly Arnold, 2018
July 24, 2018 15:30   
33. Доказуемо рекурсивные функции, занятие 2
L. D. Beklemishev
Summer School "Contemporary Mathematics" named Vitaly Arnold, 2018
July 22, 2018 11:15   
34. Доказуемо рекурсивные функции, занятие 1
L. D. Beklemishev
Summer School "Contemporary Mathematics" named Vitaly Arnold, 2018
July 21, 2018 17:15   
35. Об универсальной модели Крипке для позитивной логики доказуемости с операторами, выражающими консервативность
L. D. Beklemishev
Seminar of the Department of Mathematical Logic "Algorithmic problems in algebra and logic"
October 24, 2017 18:30
36. Модель Игнатьева как универсальная алгебра для замкнутого фрагмента позитивной логики доказуемости с операторами консервативности
L. D. Beklemishev
Seminars "Proof Theory" and "Logic Online Seminar"
March 13, 2017 18:30
37. О позитивной логике доказуемости с операторами консервативности
L. D. Beklemishev
Seminars "Proof Theory" and "Logic Online Seminar"
November 28, 2016 18:30
38. О позитивной логике доказуемости с операторами консервативности
L. D. Beklemishev
Seminars "Proof Theory" and "Logic Online Seminar"
November 21, 2016 18:30
39. О позитивной логике доказуемости с операторами, выражающими консервативность
L. D. Beklemishev
Seminar of the Department of Mathematical Logic "Algorithmic problems in algebra and logic"
November 1, 2016 18:30
40. Strictly positive fragments of modal and description logic
L. D. Beklemishev
Colloquium of the Faculty of Computer Science
September 20, 2016 18:10
41. Доказуемость и модальная логика. Занятие 4
L. D. Beklemishev
Summer School "Contemporary Mathematics", 2016
July 27, 2016 11:15   
42. Доказуемость и модальная логика. Занятие 3
L. D. Beklemishev
Summer School "Contemporary Mathematics", 2016
July 26, 2016 15:30   
43. Доказуемость и модальная логика. Занятие 2
L. D. Beklemishev
Summer School "Contemporary Mathematics", 2016
July 24, 2016 11:15   
44. Доказуемость и модальная логика. Занятие 1
L. D. Beklemishev
Summer School "Contemporary Mathematics", 2016
July 22, 2016 11:15   
45. Positive provability logic and reflection calculus
L. D. Beklemishev
Mathematical Logic, Algebra and Computation: A two-day conference dedicated to 85-th anniversary of S. I. Adian
July 19, 2016 11:00   
46. О недавних результатах по теории WQO, представленных на конференции Well-quasiorders in Computer Science, Dagstuhl, Jan 2016 (продолжение)
L. D. Beklemishev
Seminars "Proof Theory" and "Logic Online Seminar"
March 14, 2016 18:30
47. О недавних результатах по теории WQO, представленных на конференции Well-quasiorders in Computer Science, Dagstuhl, Jan 2016
L. D. Beklemishev
Seminars "Proof Theory" and "Logic Online Seminar"
February 29, 2016 18:30
48. Логика интерпретируемости. Часть 2
L. D. Beklemishev
Seminars "Proof Theory" and "Logic Online Seminar"
November 23, 2015 18:30
49. Логика интерпретируемости. Часть 1
L. D. Beklemishev
Seminars "Proof Theory" and "Logic Online Seminar"
November 16, 2015 18:30
50. Интерпретации моделей и логических теорий
L. D. Beklemishev
MIPT Interdepartmental Seminar on Discrete Mathematics
October 21, 2015
51. О медленно сходящихся системах подстановок термов в логике первого порядка (по совместной работе с А.А. Оноприенко; продолжение)
L. D. Beklemishev
Seminar of the Department of Mathematical Logic "Algorithmic problems in algebra and logic"
May 19, 2015 18:30
52. О медленно сходящихся системах подстановок термов в логике первого порядка (по совместной работе с А.А. Оноприенко)
L. D. Beklemishev
Seminar of the Department of Mathematical Logic "Algorithmic problems in algebra and logic"
May 12, 2015 18:30
53. Positive logic for reflection principles in arithmetic
L. D. Beklemishev
Steklov Mathematical Institute Seminar
January 22, 2015 16:00   
54. Positive logic for reflection principles in arithmetic
L. D. Beklemishev
Scientific session of the Steklov Mathematical Institute dedicated to the results of 2014
November 12, 2014 12:00   
55. Доказуемость и разреженная топология
L. D. Beklemishev
MIPT Interdepartmental Seminar on Discrete Mathematics
October 22, 2014
56. Элементарная геометрия с точки зрения логики. Лекция 3
L. D. Beklemishev
Summer School "Contemporary Mathematics", 2014
July 23, 2014 17:00   
57. Элементарная геометрия с точки зрения логики. Лекция 2
L. D. Beklemishev
Summer School "Contemporary Mathematics", 2014
July 21, 2014 11:15   
58. Элементарная геометрия с точки зрения логики. Лекция 1
L. D. Beklemishev
Summer School "Contemporary Mathematics", 2014
July 20, 2014 17:00   
59. О позитивных логиках доказуемости
L. D. Beklemishev
Seminar of the Department of Mathematical Logic "Algorithmic problems in algebra and logic"
December 10, 2013 18:30
60. Probably recursive functions
L. D. Beklemishev
Colloquium of Steklov Mathematical Institute of Russian Academy of Sciences
December 5, 2013 16:00   
61. Что такое логика доказуемости?
L. D. Beklemishev
Summer School "Contemporary Mathematics", 2013
July 21, 2013 12:45   
62. Прогрессии Тьюринга
L. D. Beklemishev
MIPT Interdepartmental Seminar on Discrete Mathematics
April 17, 2013 18:30   
63. On an arithmetically complete calculus for uniform reflection schemata
L. D. Beklemishev
Seminar of the Department of Mathematical Logic "Algorithmic problems in algebra and logic"
March 19, 2013 18:30
64. Fast-growing functions (“Faster, higher, stronger”). Lecture 4
L. D. Beklemishev
Summer School "Contemporary Mathematics", 2012
July 26, 2012 15:30   
65. Fast-growing functions (“Faster, higher, stronger”). Lecture 3
L. D. Beklemishev
Summer School "Contemporary Mathematics", 2012
July 25, 2012 15:30   
66. Fast-growing functions (“Faster, higher, stronger”). Lecture 2
L. D. Beklemishev
Summer School "Contemporary Mathematics", 2012
July 24, 2012 11:15   
67. Fast-growing functions (“Faster, higher, stronger”). Lecture 1
L. D. Beklemishev
Summer School "Contemporary Mathematics", 2012
July 22, 2012 17:00   
68. Fast-growing functions (“Faster, higher, stronger”). Introductory lecture
L. D. Beklemishev
Summer School "Contemporary Mathematics", 2012
July 21, 2012 11:15   
69. Алгебры доказуемости
L. D. Beklemishev
Meetings of the Moscow Mathematical Society
February 28, 2012 18:30
70. Provability algebras
L. D. Beklemishev
Globus Seminar
February 16, 2012 15:40   
71. Provability algebra and sparse topology
L. D. Beklemishev
Traditional Christmas session MIAN-POMI, 2009 "Logic and Theoretical Computer Science"
December 17, 2009 12:50   
72. Provability algebras and fragments of arithmetic
L. D. Beklemishev
Steklov Mathematical Institute Seminar
October 19, 2006 16:00   

Books in Math-Net.Ru
  1. Algorithmic aspects of algebra and logic, Collected papers. Dedicated to Academician Sergei Ivanovich Adian on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 274, ed. L. D. Beklemishev, E. F. Mishchenko, 2011, 351 с.
    http://mi.mathnet.ru/book1359

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