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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Recursive functions and intuitionistic number theory
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by David Nelson PDF
Trans. Amer. Math. Soc. 61 (1947), 307-368 Request permission

Erratum: Trans. Amer. Math. Soc. 61 (1947), 556.
References
    Paul Bernays, Logical calculus, Mimeographed lecture notes, Institute for Advanced Study, Princeton, 1936.
  • Alonzo Church, A set of postulates for the foundation of logic, Ann. of Math. (2) 33 (1932), no. 2, 346–366. MR 1503059, DOI 10.2307/1968337
  • Alonzo Church, An Unsolvable Problem of Elementary Number Theory, Amer. J. Math. 58 (1936), no. 2, 345–363. MR 1507159, DOI 10.2307/2371045
  • Gerhart Gentzen, Untersuchungen über das logische Schliessen, Math. Zeit. vol. 39 (1934) pp. 176-210
  • Kurt Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatsh. Math. Phys. 38 (1931), no. 1, 173–198 (German). MR 1549910, DOI 10.1007/BF01700692
  • —, Zur intuilionistischen Arithmetik und Zahlentheorie, Erbegnisse eines mathematischen Kolloquiums, vol. 4 (for 1931-1932, published 1933) pp. 34-38. —, On undecidable propositions of formal mathematical systems, Mimeographed lecture notes, Institute for Advanced Study, Princeton, 1934. Arend Heyting, Die formalen Regeln der intuitionistischen Logik, Preuss. Akad. Wiss. Sitzungsber. 1930, pp. 42-56. —, Die formalen Regeln der intuitionistischen Mathematik, Ibid. pp. 57-71, 158-169. David Hilbert and Paul Bernays, Grundlagen der Mathematik, Springer, Berlin, vol. 1, 1934, vol. 2, 1939.
  • S. C. Kleene, General recursive functions of natural numbers, Math. Ann. 112 (1936), no. 1, 727–742. MR 1513071, DOI 10.1007/BF01565439
  • —, On notation for ordinal numbers, Journal of Symbolic Logic vol. 3 (1938) pp. 150-155.
  • S. C. Kleene, Recursive predicates and quantifiers, Trans. Amer. Math. Soc. 53 (1943), 41–73. MR 7371, DOI 10.1090/S0002-9947-1943-0007371-8
  • S. C. Kleene, On the forms of the predicates in the theory of constructive ordinals, Amer. J. Math. 66 (1944), 41–58. MR 9757, DOI 10.2307/2371894
  • S. C. Kleene, On the interpretation of intuitionistic number theory, J. Symbolic Logic 10 (1945), 109–124. MR 15346, DOI 10.2307/2269016
  • Rózsa Péter, Über den Zusammenhang der verschiedenen Begriffe der rekursiven Funktion, Math. Ann. vol. 110 (1934) pp. 612-632.
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Additional Information
  • © Copyright 1947 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 61 (1947), 307-368
  • MSC: Primary 02.0X
  • DOI: https://doi.org/10.1090/S0002-9947-1947-0025420-1
  • MathSciNet review: 0025420