Abstract
Let L be an extension of the language of arithmetic, F 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 if and only if V contains all L-definable functions.
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References
A. Yu. Konovalov and V. E. Plisko, “On Hyperarithinetical Realizability,” Matern. Zametki 98 (5), 725 (2015) [Math. Notes 98 (5), 778 (2015)].
A. Yu. Konovalov., “Arithmetical Realizability and Basic Logic,” Vestn. Mosk. Univ., Matem. Mekhan., No. 1, 52 (2016).
S. Salehi, “Provably Total Functions of Basic Arithmetic,” Math. Log. Quart. 49 (3), 316 (2003).
S. C. Kleene, Introduction to Metamathematics (Wolters-Noordhoff, 1952; IL, Moscow, 1957).
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Russian Text © The Author(s). 2019. published in Vestnik Moskovskogo Universiteta. Matematika. Mekhanika. 2019, Vol. 74, No. 4, pp. 50–54.
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Konovalov, A.Y. Generalized Realizability for Extensions of the Language of Arithmetic. Moscow Univ. Math. Bull. 74, 167–170 (2019). https://doi.org/10.3103/S0027132219040065
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DOI: https://doi.org/10.3103/S0027132219040065