Geodesic
Model Approach to Nonstandard Analysis in the Context of Axiomatic Set Theory
Matematičeskie zametki, Tome 79 (2006) no. 1, pp. 134-141

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In this paper, the model approach to nonstandard analysis is developed on the basis of Zermelo–Fraenkel axiomatic set theory with atoms. The traditional consideration of the standard superstructure $V$ as the primary object of nonstandard analysis is justified. Set-theoretic axioms for the nonstandard system $*V$ are obtained. 
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     author = {I. V. Yakovlev},
     title = {Model {Approach} to {Nonstandard} {Analysis} in the {Context} of {Axiomatic} {Set} {Theory}},
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I. V. Yakovlev. Model Approach to Nonstandard Analysis in the Context of Axiomatic Set Theory. Matematičeskie zametki, Tome 79 (2006) no. 1, pp. 134-141. http://geodesic.mathdoc.fr/item/MZM_2006_79_1_a11/