## Journal of Symbolic Logic

### On Automorphism Groups of Countable Structures

Su Gao

#### Abstract

Strengthening a theorem of D.W. Kueker, this paper completely characterizes which countable structures do not admit uncountable L$_{\omega_1\omega}$-elementarily equivalent models. In particular, it is shown that if the automorphism group of a countable structure M is abelian, or even just solvable, then there is no uncountable model of the Scott sentence of M. These results arise as part of a study of Polish groups with compatible left-invariant complete metrics.

#### Article information

Source
J. Symbolic Logic, Volume 63, Issue 3 (1998), 891-896.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745572

Mathematical Reviews number (MathSciNet)
MR1649067

Zentralblatt MATH identifier
0922.03045

JSTOR