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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An intuitionistic definition of classical natural numbers
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by Vladimir Lifschitz
Proc. Amer. Math. Soc. 77 (1979), 385-388
DOI: https://doi.org/10.1090/S0002-9939-1979-0545601-4
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Abstract:

A definition of natural numbers in the theory of species is given which allows us to prove intuitionistically all theorems of classical arithmetic. This provides an alternative to the well-known Gödel negative translation.
References
  • A. S. Troelstra, Intuitionistic formal systems, Metamathematical investigation of intuitionistic arithmetic and analysis, Lecture Notes in Math., Vol. 344, Springer, Berlin, 1973, pp. 1–96. MR 0444439
    • V. Lifschitz, A conservative extension of $H{A^c}$ with the E-property, Notices Amer. Math. Soc. 25 (1978), A-362.
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Bibliographic Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 77 (1979), 385-388
  • MSC: Primary 03F35
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0545601-4
  • MathSciNet review: 545601