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Arithmetical realizability and basic logic

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Abstract

Absolute arithmetical realizability of predicate formulas is introduced. It is proved that the intuitionistic logic is not correct with this semantics, but the basic logic is correct.

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References

  1. S. C. Kleene, Introduction to Metamathematics (Wolters-Noordhoff, 1952; IL, Moscow, 1957).

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  2. V. E. Plisko, “Absolute Realizability of Predicate Formulas,” Izvestiya Akad. Nauk SSSR, Matem. 47 (2), 315 (1983).

    MathSciNet  Google Scholar 

  3. W. Ruitenburg, “Basic Predicate Calculus,” Notre Dame J. Formal Logic 39 (1), 18 (1998).

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  4. S. Salehi, “Primitive Recursive Realizability and Basic Arithmetic,” Bull. Symbol. Logic 7 (1), 147 (2001).

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    A. Yu. Konovalov

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  1. A. Yu. Konovalov
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Correspondence to A. Yu. Konovalov.

Additional information

Original Russian Text © A. Y-u. Konovalov, 2016, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2016, Vol. 71, No. 1, pp. 52-56.

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Konovalov, A.Y. Arithmetical realizability and basic logic. Moscow Univ. Math. Bull. 71, 35–38 (2016). https://doi.org/10.3103/S0027132216010071

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  • DOI: https://doi.org/10.3103/S0027132216010071

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