Geodesic
Model Approach to Nonstandard Analysis in the Context of Axiomatic Set Theory
Matematičeskie zametki, Tome 79 (2006) no. 1, pp. 134-141 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Devis M., Prikladnoi nestandartnyi analiz, Mir, M., 1980 | MR

[2] Albeverio S., Fenstad I., Kheeg-Kron R., Lindstrem T., Nestandartnye metody v stokhasticheskom analize i matematicheskoi fizike, Mir, M., 1990 | MR | Zbl

[3] Nonstandard Analysis for the Working Mathematician, eds. Loeb P., Wolff M. P. H., Kluwer, Dordrecht, 2000 | MR

[4] Nelson E., “Internal set theory: a new approach to nonstandard analysis”, Bull. Amer. Math. Soc., 83:6 (1977), 1165–1198 | DOI | MR | Zbl

[5] Gordon E. I., Kusraev A. G., Kutateladze S. S., Infinitezimalnyi analiz, Ch. 1, Izd-vo IM, Novosibirsk, 2001

[6] Yakovlev V. F., “Rasshirennyi universum dlya sistem s minimalnymi strukturami”, Dokl. AN SSSR, 319:1 (1991), 103–105 | MR | Zbl

[7] Iekh T., Teoriya mnozhestv i metod forsinga, Mir, M., 1973 | MR

[8] Keisler G., Chen Ch. Ch., Teoriya modelei, Mir, M., 1977 | MR

[9] Makkai M., “Dopustimye mnozhestva i beskonechnaya logika”, Spravochnaya kniga po matematicheskoi logike, Ch. 1, Nauka, M., 1982, 235–288