Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-05-02T07:25:00.407Z Has data issue: false hasContentIssue false
  • English
  • Français

The strength of the isomorphism property

Published online by Cambridge University Press:  12 March 2014

Renling Jin  and
Saharon Shelah
Renling Jin
Affiliation:
Department of Mathematics, University of of California, Berkeley, California 94720
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Get access Rights & Permissions [Opens in a new window]

Abstract

In § 1 of this paper, we characterize the isomorphism property of nonstandard universes in terms of the realization of some second-order types in model theory. In §2, several applications are given. One of the applications answers a question of D. Ross in [this Journal, vol. 55 (1990), pp. 1233–1242] about infinite Loeb measure spaces.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 1 , March 1994 , pp. 292 - 301
Copyright
Copyright © Association for Symbolic Logic 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[CK] Chang, C. C. and Keisler, H. J., Model Theory, North-Holland, Amsterdam, 1983; third edition, 1990.Google Scholar
[H1] Henson, C. W., The isomorphism property in nonstandard analysis and its use in the theory of Banach space, this Journal, vol. 39 (1974), pp. 717–731.Google Scholar
[H2] Henson, C. W., When do two Banach spaces have isometrically isomorphic nonstandard hulls, Israel Journal of Mathematics, vol. 22 (1975), pp. 57–67.CrossRefGoogle Scholar
[H3] Henson, C. W., Unbounded Loeb measures, Proceedings of the American Mathematical Society, vol. 74 (1979), pp. 143–150.CrossRefGoogle Scholar
[J1] Jin, R., The isomorphism property versus the special model axiom, this Journal, vol. 57 (1992), pp. 975–987.Google Scholar
[J2] Jin, R., A theorem on the isomorphism property, this Journal, vol. 57 (1992), pp. 1011–1017.Google Scholar
[JK] Jin, R. and Keisler, H. J., Game sentences and ultrapowers, Annals of Pure and Applied Logic, vol. 60 (1993), pp. 261–274.CrossRefGoogle Scholar
[L] Loeb, P., Conversion from nonstandard to standard measure space and applications in probability theory, Transactions of the American Mathematical Society, vol. 211 (1975), pp. 113–122.CrossRefGoogle Scholar
[R] Ross, D., The special model axiom in nonstandard analysis, this Journal, vol. 55 (1990), pp. 1233–1242.Google Scholar
[S] Shelah, S., Every two elementarily equivalent models have isomorphic ultrapowers, Israel Journal of Mathematics, vol. 10 (1971), pp. 224–233.CrossRefGoogle Scholar
[SB] Stroyan, K. D. and Bayod, J. M., Foundation of Infinitesimal Stochastic Analysis, North-Holland, Amsterdam, 1986.Google Scholar