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Beklemishev Lev Dmitrievich
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: https://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.


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

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© Steklov Math. Inst. of RAS, 2024