Abstract
We study those models of ZFCwhich are embeddable, as the class of all standard sets, in a model of internal set theory >ISTor models of some other nonstandard set theories.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Felgner, U., 1971, ‘Comparison of the axioms of local and universal choice’, Fund. Math. 71, 43-62.
HrbaČek, K., 1978, ‘Axiomatic foundations for nonstandard analysis’, Fund. Math. 98, 1-19.
HrbaČek, K., 1979, ‘Nonstandard set theory’, Amer. Math. Monthly 86, 659-677.
Kanovei, V., 1991, ‘Undecidable hypotheses in Edward Nelson's internal set theory’, Russian Math. Surveys 46,no. 6, 1-54.
Kanovei, V., and M. Reeken, 1995, ‘Internal approach to external sets and universes’, Studia Logica 55,no. 2, 227-235, 55, no. 3, 347–376, and 1996, 56, no. 3, 293–322.
Kanovei V., and M. Reeken, 1997, ‘Mathematics in a nonstandard world’, Math. Japonica 45,no. 2, 369-408 and no. 3, 555–571.
KawaÏ, T., 1981, ‘Axiom systems of nonstandard set theory’, Logic Symposia Hakone 1979, 1980 (Lecture Notes in Mathematics, 891), Springer, 1981, 57-64.
KawaÏ, T., 1983, ‘Nonstandard analysis by axiomatic methods’, Southeast Asia Conference on Logic, Singapore 1981 (Studies in Logic and Foundations of Mathematics, 111) North Holland, 1983, 55-76.
Nelson, E., 1977, ‘Internal set theory: a new approach to nonstandard analysis’, Bull. Amer. Math. Soc. 83, 1165-1198.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kanovei, V., Reeken, M. Extending Standard Models of ZFC to Models of Nonstandard Set Theories. Studia Logica 64, 37–59 (2000). https://doi.org/10.1023/A:1005286212737
Issue Date:
DOI: https://doi.org/10.1023/A:1005286212737