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An intuitionistic definition of classical natural numbers


Author: Vladimir Lifschitz
Journal: Proc. Amer. Math. Soc. 77 (1979), 385-388
MSC: Primary 03F35
MathSciNet review: 545601
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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 [Enhancements On Off] (What's this?)

  • [1] A. S. Troelstra, Intuitionistic formal systems, Metamathematical investigation of intuitionistic arithmetic and analysis, Springer, Berlin, 1973, pp. 1–96. Lecture Notes in Mathematics, Vol. 344. MR 0444439
  • [2] 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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0545601-4
Keywords: Intuitionistic logic, theory of species
Article copyright: © Copyright 1979 American Mathematical Society