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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: [email protected]
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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

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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