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On certain theorems of analysis in the formal system Kleene-Vesley

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Abstract

It is proven that in the Kleene-Vesley formal system of intuitionistic analysis, theorems on upper bounds and on mean values of functions can neither be deduced nor verified.

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Literature cited

  1. S. C. Kleene and R. E. Vesley, Foundations of Intuitionistic Mathematics, North-Holland Publishing Co., Amsterdam (1965).

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  2. S. C. Kleene, Introduction to Metamathematics, Van Nostrand, Princeton, N. J. (1952).

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  3. A. Heyting, Intuitionism: An Introduction (3rd edition), North-Holland Publishing Co., London (1971).

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  4. A. G. Dragalin, “Computability of primitive recursive terms of finite type and primitive recursive realization,” Zap. Nauch. Seminarov, Leningr. Otd. Matem. In-ta im. Steklova,8, 32–45 (1968).

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  5. G. S. Tseitin, “Mean-value theorems in constructive analysis,” Tr. Mat. Inst. Akad. Nauk SSSR,67, 362–384 (1962).

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Authors and Affiliations

  1. Computer Center, Academy of Sciences, ArmSSR

    M. A. Khachatryan

Authors
  1. M. A. Khachatryan
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Additional information

Translated from Matematicheskie Zametki, Vol. 21, No. 1, pp. 109–116, January, 1977.

The author wishes to thank A. G. Dragalin for having posed the problem and fr his interest in the work.

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Khachatryan, M.A. On certain theorems of analysis in the formal system Kleene-Vesley. Mathematical Notes of the Academy of Sciences of the USSR 21, 60–64 (1977). https://doi.org/10.1007/BF02317038

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  • DOI: https://doi.org/10.1007/BF02317038

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