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Recursive functions and intuitionistic number theory


Author: David Nelson
Journal: Trans. Amer. Math. Soc. 61 (1947), 307-368
MSC: Primary 02.0X
DOI: https://doi.org/10.1090/S0002-9947-1947-0025420-1
Erratum: Trans. Amer. Math. Soc. 61 (1947), 556.
MathSciNet review: 0025420
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  • [1] Paul Bernays, Logical calculus, Mimeographed lecture notes, Institute for Advanced Study, Princeton, 1936.
  • [2] Alonzo Church, A set of postulates for the foundation of logic, Ann. of Math. (2) vol. 33 (1932) pp. 346-366 MR 1503059
  • [3] -, An unsolvable problem of elementary number theory, Amer. J. Math. vol. 58 (1936) pp. 345-363. MR 1507159
  • [4] Gerhart Gentzen, Untersuchungen über das logische Schliessen, Math. Zeit. vol. 39 (1934) pp. 176-210
  • [5] Kurt Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatshefte für Mathematik und Physik vol. 38 (1931) pp. 173-198. MR 1549910
  • [6] -, Zur intuilionistischen Arithmetik und Zahlentheorie, Erbegnisse eines mathematischen Kolloquiums, vol. 4 (for 1931-1932, published 1933) pp. 34-38.
  • [7] -, On undecidable propositions of formal mathematical systems, Mimeographed lecture notes, Institute for Advanced Study, Princeton, 1934.
  • [8] Arend Heyting, Die formalen Regeln der intuitionistischen Logik, Preuss. Akad. Wiss. Sitzungsber. 1930, pp. 42-56.
  • [9] -, Die formalen Regeln der intuitionistischen Mathematik, Ibid. pp. 57-71, 158-169.
  • [10] David Hilbert and Paul Bernays, Grundlagen der Mathematik, Springer, Berlin, vol. 1, 1934, vol. 2, 1939.
  • [11] S. C. Kleene, General recursive functions of natural numbers, Math. Ann. vol. 112 (1936) pp. 727-742. MR 1513071
  • [12] -, On notation for ordinal numbers, Journal of Symbolic Logic vol. 3 (1938) pp. 150-155.
  • [13] -, Recursive predicates and quantifiers, Trans. Amer. Math. Soc. vol. 53 (1943) pp. 41-73. MR 0007371 (4:126b)
  • [14] -, On the forms of the predicates in the theory of constructive ordinals, Amer. J. Math. vol. 66 (1944) pp. 41-58. Errata: p. 43, line 12 read ``(4)'' instead of ``(4*)"; p. 54, line 4, read "a" instead of "e." MR 0009757 (5:197e)
  • [15] -, On the interpretation of intuitionistic number theory, Journal of Symbolic Logic vol. 10 (1945) pp. 109-124. MR 0015346 (7:406a)
  • [16] Rózsa Péter, Über den Zusammenhang der verschiedenen Begriffe der rekursiven Funktion, Math. Ann. vol. 110 (1934) pp. 612-632.

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DOI: https://doi.org/10.1090/S0002-9947-1947-0025420-1
Article copyright: © Copyright 1947 American Mathematical Society

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