Geodesic
Generalized realizability for extensions of arithmetic language
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2019), pp. 50-54 
A. Yu. Konovalov. Generalized realizability for extensions of arithmetic language. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2019), pp. 50-54. http://geodesic.mathdoc.fr/item/VMUMM_2019_4_a7/
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     author = {A. Yu. Konovalov},
     title = {Generalized realizability for extensions of arithmetic language},
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     year = {2019},
     number = {4},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_4_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $L$ be an extension of the language of arithmetic, $V$ be a class of number-theoretical functions. A notion of the $V$-realizability for $L$-formulas is defined in such a way that indexes of functions in $V$ are used for interpreting the implication and the universal quantifier. It is proved that the semantics for $L$ based on the $V$-realizability coincides with the classic semantics iff $V$ contains all $L$-definable functions.

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