Journal of Symbolic Logic

On Automorphism Groups of Countable Structures

Su Gao

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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

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745572

Mathematical Reviews number (MathSciNet)
MR1649067

Zentralblatt MATH identifier
0922.03045

JSTOR
links.jstor.org

Citation

Gao, Su. On Automorphism Groups of Countable Structures. J. Symbolic Logic 63 (1998), no. 3, 891--896. https://projecteuclid.org/euclid.jsl/1183745572


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