
1943
On special extensions of topological spaces (in Russian)
C.R. (Dokl.) Akad. Sciencies USSR, 38 (1943), 711.
On separability in topological spaces (in Russian).
C.R. (Dokl.) Akad. Sciencies USSR, 38 (1943), 188192.
On the theory of bicompact extensions of topological spaces (in Russian).
C.R. (Dokl.) Akad. Sciencies USSR, 38 (1943), 166169.
1944
On imbedding in a power of topological space (in Russian).
Izv. Akad. Nauk SSSR, Ser. Mat., 8 (1944), 233242.
1946
A theorem from the general theory of sets (in Russian).
C.R. (Dokl.) Akad. Sciencies USSR, 53 (1946), 399400.
On intersections of open subsets in the product of topological spaces (in Russian)
C.R. (Dokl.) Akad. Sciencies USSR, 53 (1946), 503506.
On the product of topological spaces (in Russian)
C.R. (Dokl.) Akad. Sciencies USSR, 53 (1946), 595598.
On dyadic bicompacts (in Russian)
C.R. (Dokl.) Akad. Sciencies USSR, 53 (1946), 785788.
1948
On the product of topological spaces (in Russian)
Trudy Mat. Inst. Steklov, Academy of Sciencies of the USSR, 24 (1948), 1112.
1952
On subsets of the set of natural numbers, that have density. (in Russian)
Mat. Sbornik, 31 (73) (1952), 367380.
1953
On some operations with logicalarithmetical formulas.(in Russian)
C.R. (Dokl.) Akad. Sciencies USSR, 93 (1953), 779782.
1954
On imbedding of the classical logicalarithmetical calculus into constructive logicalarithmetical calculus. (in Russian)
Dokl. Akad. Nauk SSSR, 94 (1954), 193196.
1955
On some logical problems of arithmetics. (in Russian)
Trudy Mat. Inst. Steklov, Academy of Sciencies of the USSR, 43 (1955),
1112.
1956
Some problems of mathematical analysis in view of constructive logic.
Z. f. math. Logik und Grundlagen der Math., 2 (1956), 2736.
On constructive understanding of mathematical judgements. (in Russian)
Proc.III AllUnion mat. Conference, vol. 1, Moscow (1956), 189190.
On constructive mathematical analysis (in Russian)
Proc.3 AllUnion mat. Conference, vol. 2, Moscow (1956), 6971.
1958
On constructive understanding of mathematical judgements. (in Russian)
Trudy Mat. Inst. Steklov, Academy of Sciencies of the USSR, 52 (1958),
226311.
On an algorithm of constructive decoding of mathematical judgments.
Z. Math. Logic Grundlagen Math., 4:4 (1958), 293303.
1959
On linear constructive functionals in the constructive Hilbert space.
Z. Math. Logic Grundlagen Math., 5:1 (1959), 18.
1962
Constructive real numbers and constructive function spaces. (in Russian)
Tr. Mat. Inst. Steklov, 67 (1962), 15294,
translated into English in 1968 .
1963
Constructive mathematical analysis. (with A.A. Markov, I.D. Zaslavsky and G.S. Tseitin, in Russian)
Proc. 4 AllUnion Mat. Conference, 1 (1963), 198.
1964
Concerning the constructive interpretation of auxiliary formulae,I. (in Russian)
Tr. Mat. Inst. Steklov, 72 (1964), 348397, translated
into English in 1972 .
1965
An algorithm for a machine scan of a natural logical deduction in a
propositional calculus. (with Davidov G.V.,
Maslov S.J., Minc G.E., Orevkov V.P. and Slisenko A.O, in Russian)
Academy of Sciencies of the USSR, Steklov Mat. Inst., Leningrad department,
"Nauka", Moscow (1965), pp140.
1966
Peculiarities of constructive mathematical analysis. (with Tsejtin G. S. and Zaslavskij I.D., in Russian)
Mezhdunar. Kongr. Mat., Moskva, (1966), 253261, translated
into English in 1968.
1968
Peculiarities of constructive mathematical analysis. (with Tsejtin G. S. and Zaslavskij I.D.)
American Math. Soc., Transl., II. Ser., 70, 1625 (1968),
translated from Trudy Mezhdunar. Kongr. Mat., Moskva, 1966.
Constructive real numbers and constructive function spaces.
Translations of Mathematical Monographs. 21. Providence, RI: Amer. Math. Soc.,
IV, 325p (1968), translated from Russian original, published in 1962.
1970
On recursive mathematical analysis and R.L. Goodstein calculus of equalities. (in Russian)
In the book by R.L.Goodstein "Recursive mathematical analysis", Moscow, Nauka
(1970), pp 776.
On narrow constructive semantics of arithmetical judgments.
Commun. Indiv., Congress Intern. des Math., Nice, (1970), 2.
1972
Conserning the constructive interpretation of auxiliary formulas.
Amer. Mathematical Society Translations, Series 2,
99 AMS, Providence, 1972, p 233275, translated from Russian original, published in 1964.
1973
On a hierarchy of methods of interpreting propositions in constructive
mathematics. (in Russian)
Trudy Math. Inst. Steklov, 129 (1973), 203266,
translated into English in 1976.
1974
A hierarchy of Brouwer constructive functionals.(in Russian)
Zap. Nauchn. Semin. Lening. Otd. Mat. Inst. Steklov, 40 (1974),
142147, translated into English in 1977.
1976
On the quantifier of limiting realizability.
Journal of Mathematiacl Sciences, vol. 14, no. 5, pp. 15651572.
Translated from Zap. Nauchn. Semin. Lening. Otd. Mat. Inst. Steklov,
60 (1976), 209220,
translated into English in 1980.
On a hierarchy of methods of interpreting propositions in constructive
mathematics.
Proc. Steklov Inst. Math., 209271 (1976), translated from Russian original, published in 1973.
1977
On the quantifier of limiting realizability.
Proc. of Symposium. Set. theory, Foundations of mathematics. Beograd (1977),
127.
Mathematics and philosophy.
Proc. of Symposium. Set. theory, Foundations of mathematics. Beograd (1977),
139152.
A hierarchy of Brouwer constructive functionals.
J. Sov. Math. 8, 345348 (1977) [ISSN 00904104], translated from Russian original, published in 1974.
1979
On canonical recursive functions and operations.
( in Russian)
Zapiski Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova, 88 (1979),
218235, translated into English in 1982.
The Notion of canonical recursive function as an alternative to the notion
of recursive program. (in Russian)
5th AllUnion conference on mathematical logic. Novosibirsk (1979), 164.
1980
On the quantifier of limiting realizability.
J. Sov. Math. 14, 15651572 (1980) [ISSN 00904104], translated from Russian original, published in 1976.
1981
Role of the notion of algorithm in arithmetic language semantics.
Lect. Notes Comput. Sci. 122 (1981), Russian version was published in 1982.
1982
On semantically simple variants of constructive mathematical analysis.(in Russian)
8th AllUnion conference "Logic and methodology of science." Section "Logic
and foundations of mathematics". Vilnius (1982), 99104.
Role of a notion of algorithm in the semantics of arithmetic languages (in Russian)
Algorithms in modern mathematics, II, Mater. Int. Symp., (Urgench/ UzSSR, 1979, Novosibirsk, 1982), 147180, English version was published in 1981.
On majorization of theorems of constructive mathematics by semantically
simple propositions.
Short communications (Abstracts). 1. Section Math. logic and foundations of
mathematics. Warszawa: ICM. (1982), 21.
Canonical recursive fuunctions and operations.
J. Sov. Math. 20, 23812390 (1982) [ISSN 00904104], translated from Russian original, published in 1979.
1983
Ob "algoritmicheskom podtekste" teorii mnozhestv s klassicheskim
kvantorom sushchestvovanija.
(in Russian)
III conference "Usage of Methods of mathematical logic". Tallinn (1983),
115116.
1984
On finitization of mathematical analysis. (in Russian)
7th AllUnion conference on mathematical logic. Novosibirsk (1984), 198199.
1987
On finitary development of mathematical analysis on the base of Euler's notion of function. (in Russian)
7th international congress on logic, methodology and philosophy of science.
Abstracts. Moscow 1 (1987), p 6063.
1988
Finitary version of the notion of generalized function.
Intern. conf. on comp. logic (COLOG88). Abstracts. Tallinn 1 (1988),
99100.
1997
Georg Cantor as the author of constructions that play fundamental roles in constructive mathematics
Journal of Mathematical Sciences, vol. 87, no. 1, 1997. Translated from
Zap. Nauchn. Sem. SanktPeterburg. Otdel. Mat. Inst. Steklov (POMI), 220(1995), Issled. po
konstrukt. Mat. i mat Logike. 1 IX, p 522, 145.
1998
On procedure approach to explanation of sence of judgements.
(in Russian)
5th national scientific conference "Modern logic: problems of theory, history
and usage in science", St. Petersburg, 1998,
p 415421.
2000
A sketch of a finitary version of mathematical analysis. (in Russian)
Preprint POMI
[ Full text:
(.ps.gz),
(.tex),
(.dvi) ]
2001
On a finitary version of mathematical analysis.
Annals of Pure and Applied Logic, v. 113, no. 13, 2001, pp. 261295.
2008
On base representations of finitary mathematics.
Methods of Logic in Mathematics, III. Abstracts. P. 1416. St. Petersburg, 2006.
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