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Modified realizability and predicate logic

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Abstract

Semantics of predicate formulas based on the notion of modified realizability for arithmetic formulas and interpretations of the language of arithmetic in all finite types are considered. For a number of natural constructive interpretations, the corresponding predicate logic of modified realizability is proved to be nonarithmetical.

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Authors and Affiliations

  1. M. V. Lomonosov, Moscow State University, USSR

    V. E. Plisko

Authors
  1. V. E. Plisko
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Additional information

Translated fromMatematicheskie Zametki, Vol. 61, No. 2, pp. 259–269, February, 1997.

This research was supported by the Russian Foundation for Basic Research under grant No. 95-01-00416 and by the International Science Foundation under grant No. NFQ000.

Translated by V. N. Dubrovsky

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Plisko, V.E. Modified realizability and predicate logic. Math Notes 61, 212–220 (1997). https://doi.org/10.1007/BF02355731

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