Journal of Symbolic Logic

The Isomorphism Property Versus the Special Model Axiom

Renling Jin

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Abstract

This paper answers some questions of D. Ross in [R]. In $\S 1$, we show that some consequences of the $\aleph_0$- or $\aleph_1$-special model axiom in [R] cannot be proved by the $\kappa$-isomorphism property for any cardinal $\kappa$. In $\S 2$, we show that with one exception, the $\aleph_0$-isomorphism property does imply the remaining consequences of the special model axiom in [R]. In $\S 3$, we improve a result in [R] by showing that the $\kappa$-special model axiom is equivalent to the $\aleph_0$-special model axiom plus $\kappa$-saturation.

Article information

Source
J. Symbolic Logic, Volume 57, Issue 3 (1992), 975-987.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183744052

Mathematical Reviews number (MathSciNet)
MR1187460

Zentralblatt MATH identifier
0770.03025

JSTOR
links.jstor.org

Citation

Jin, Renling. The Isomorphism Property Versus the Special Model Axiom. J. Symbolic Logic 57 (1992), no. 3, 975--987. https://projecteuclid.org/euclid.jsl/1183744052


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