Journal of Symbolic Logic

The Strength of the Isomorphism Property

Renling Jin and Saharon Shelah

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In $\S 1$ 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 $\S 2$, 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.

Article information

J. Symbolic Logic, Volume 59, Issue 1 (1994), 292-301.

First available in Project Euclid: 6 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 03C50: Models with special properties (saturated, rigid, etc.)
Secondary: 03H05: Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05] 26E35: Nonstandard analysis [See also 03H05, 28E05, 54J05] 28E05: Nonstandard measure theory [See also 03H05, 26E35]


Jin, Renling; Shelah, Saharon. The Strength of the Isomorphism Property. J. Symbolic Logic 59 (1994), no. 1, 292--301.

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