Journal of Symbolic Logic

On Automorphism Groups of Countable Structures

Su Gao

Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR.


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

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

First available in Project Euclid: 6 July 2007

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier



Gao, Su. On Automorphism Groups of Countable Structures. J. Symbolic Logic 63 (1998), no. 3, 891--896.

Export citation