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On automorphism groups of countable structures

Published online by Cambridge University Press:  12 March 2014

Su Gao
Su Gao*
Affiliation:
Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90024, USA E-mail: sgao@math.ucla.edu
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Abstract

Strengthening a theorem of D. W. Kueker, this paper completely charaterizes which countable structures do not admit uncountable Lω1ω-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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 3 , September 1998 , pp. 891 - 896
Copyright
Copyright © Association for Symbolic Logic 1998

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References

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