Geodesic
Nonconstructivizable formal arithmetic structures
Izvestiya. Mathematics , Tome 30 (1988) no. 1, pp. 103-122.

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Nonconstructivizability of a number of formal arithmetric structures is established in nonstandard models of formal Peano arithmetric ($PA$). Also considered is a formal structure whose constructivizability in a countable nonstandard model of $PA$ depends on the choice of the model. All concrete examples are built on formulas of class $\Delta_1(PA)$. Therefore the standard interpretations are recursive. Bibliography: 12 titles. 
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A. A. Tverskoi. Nonconstructivizable formal arithmetic structures. Izvestiya. Mathematics , Tome 30 (1988) no. 1, pp. 103-122. http://geodesic.mathdoc.fr/item/IM2_1988_30_1_a5/

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