Journal of Symbolic Logic

A Theorem on the Isomorphism Property

Renling Jin

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An $\mathscr{L}$-structure is called internally presented in a nonstandard universe if its base set and interpretation of every symbol in $\mathscr{L}$ are internal. A nonstandard universe is said to satisfy the $\kappa$-isomorphism property if for any two internally presented $\mathscr{L}$-structures $\mathfrak{U}$ and $\mathfrak{B}$, where $\mathscr{L}$ has less than $\kappa$ many symbols, $\mathfrak{U}$ is elementarily equivalent to $\mathfrak{B}$ implies that $\mathfrak{U}$ is isomorphic to $\mathfrak{B}$. In this paper we prove that the $\aleph_1$-isomorphism property is equivalent to the $\aleph_0$-isomorphism property plus $\aleph_1$-saturation.

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J. Symbolic Logic, Volume 57, Issue 3 (1992), 1011-1017.

First available in Project Euclid: 6 July 2007

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Jin, Renling. A Theorem on the Isomorphism Property. J. Symbolic Logic 57 (1992), no. 3, 1011--1017.

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