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THE EVOLUTION OF…

The Constructive Mathematics of A. A. Markov

Pages 559-566 | Published online: 31 Jan 2018

REFERENCES

  • E. Bishop, Foundations of Constructive Analysis McGraw-Hill, New York, 1967.
  • E. Borel, Le calcul des integrales définies, J. math. pures et appliquees 8 (1912) 159–210.
  • E. Borel, Leçons sur la théorie des functions, 3rd ed., Gauthier-Villars, Paris, 1928.
  • A. Grzegorczyk, Computable functionals, Fund. Math. 42 (1955) 168–202.
  • R. L. Goodstein, Recursive Number Theory, North-Holland, Amsterdam, 1957.
  • R. L. Goodstein, Recursive Analysis. North-Holland, Amsterdam, 1961.
  • P. Hertling, A Banach-Mazur computable but not Markov computable function on the computable real numbers, in Automata, Languages and Programming, P. Widmayer, F. Triguero, et al., eds., Springer-Verlag, Berlin, 2002, pp. 962–972.
  • A. Heyting, Intuitionism. An Introduction, North-Holland, Amsterdam, 1956.
  • A. Heyting, After thirty years, in Logic, Methodology and Philosophy of Science, Proceedings of the 1960 International Congress, E. Nagel et al., eds., Stanford University Press, Palo Alto, 1962, pp. 194–197.
  • A. N. Kolmogorov, O printsipe tertium non datur Mat. Sbornik 32 (1925) 646–667 (Russian); translation in From Frege to Gödei: A Source-Book in Mathematical Logic, 1879–1932, J. van Heijenoort, ed., Harvard University Press, Cambridge, 1967.
  • B. A. Kushner, Lectures on Constructive Mathematical Analysis (translation from the Russian original of 1973), American Mathematical Society, Providence, 1984.
  • D. Lacombe, Extension de la notion de fonction recursive aux fonctions d'une ou plusieurs variables reeles, C.R. Acad. Sci. Paris 240 (1955) 2478–2480.
  • A. A. Markov Jr., The Theory of Algorithms, Trudy Mat. Instituta im. Steklova 42 (1954) (Russian); translation in Israel Program Sci. Transl., Jerusalem, 1961.
  • A. A. Markov Jr, O konstraktivnykh funkciyakh. Trudy Mat. Instituta im. Steklova 52 (1958) 315–348 (Russian); English translation in Amer. Math. Soc. Transl. (2) 29 (1963).
  • A. A. Markov Jr, Izbrannye Trudy (Selected Works), vols. 1 and 2. N. M. Nagorny, ed., MTsHMO. Moscow. 2002 and 2003 (Russian).
  • G. S. Tseitin, Ravnomernaya rekursivnost' algorifmicheskikh operatorov nad obscherekursivnymi funkciyami i kanonicheskoe predstavlenie dlya konstruktivnykh funkciy veschestvennogo argumenta, Trudy 3-go Vsesoyuznogo matem.s'ezda 1 (1956) 188–189 (Russian).

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