## Journal of Symbolic Logic

### A Theorem on the Isomorphism Property

Renling Jin

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183744055

Mathematical Reviews number (MathSciNet)
MR1187463

Zentralblatt MATH identifier
0769.03037

JSTOR