Abstract
A characterization of the standard models of ZFC set theory that are embeddable as the class of standard sets in models of the internal set theory IST and some of its versions is proposed.
Similar content being viewed by others
References
E. Nelson, “Internal set theory: a new approach to nonstandard analysis,”Bull. Amer. Math. Soc.,83, 1165–1198 (1977).
V. G. Kanovei, “Unsolvable conjectures in the internal set theory of Edward Nelson,”Uspekhi Mat. Nauk [Russian Math. Surveys],46, No. 6, 3–50 (1991).
K. Hrbaček, “Axiomatic foundations for nonstandard analysis,”Fund. Math.,98, 1–19 (1978).
V. Kanovei and M. Reeken, “Internal approach to external sets and universes. 1,”Studia Logica,55, No. 2, 227–235 (1995).
V. Kanovei and M. Reeken, “Mathematics in a nonstandard world,”Math. Japon.,45, No. 3, 555–571 (1997).
T. Kawaï, “Nonstandard analysis by axiomatic methods,” in:Southeast Asia Conference on Logic (Singapore 1981), Vol. 111, Stud. Logic Found. Math., North-Holland, Amsterdam (1983), pp. 55–76.
A. G. Kusraev and S. S. Kutateladze,Nonstandard Methods in Analysis [in Russian], Nauka, Novosibirsk (1990).
Author information
Authors and Affiliations
Additional information
Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 202–210, August, 1999.
Rights and permissions
About this article
Cite this article
Kanovei, V.G., Reeken, M. Extension of standard models of ZFC to models of Nelson’s nonstandard set theory IST. Math Notes 66, 160–166 (1999). https://doi.org/10.1007/BF02674872
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02674872