Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-25T16:14:50.360Z Has data issue: false hasContentIssue false
  • English
  • Français

The isomorphism property versus the special model axiom

Published online by Cambridge University Press:  12 March 2014

Renling Jin
Renling Jin*
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, E-mail: jin@math.wisc.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper answers some questions of D. Ross in [R]. In §1, we show that some consequences of the ℵ1- or ℵ1-special model axiom in [R] cannot be proved by the κ-isomorphism property for any cardinal κ. In §2, we show that with one exception, the ℵ0-isomorphism property does imply the remaining consequences of the special model axiom in [R]. In §3, we improve a result in [R] by showing that the κ-special model axiom is equivalent to the ℵ0-special model axiom plus κ-saturation.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 3 , September 1992 , pp. 975 - 987
Copyright
Copyright © Association for Symbolic Logic 1992

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, 1973 (3rd ed., 1990).Google Scholar
[H]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
[R]Ross, D., The special model axiom in nonstandard analysis, this Journal, vol. 55 (1990), pp. 1233–1242.Google Scholar