On Automorphism Groups of Countable Structures
Gao, Su
J. Symbolic Logic, Tome 63 (1998) no. 1, p. 891-896 / Harvested from Project Euclid
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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.
Publié le : 1998-09-14
Classification:  
@article{1183745572,
     author = {Gao, Su},
     title = {On Automorphism Groups of Countable Structures},
     journal = {J. Symbolic Logic},
     volume = {63},
     number = {1},
     year = {1998},
     pages = { 891-896},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745572}
}

Gao, Su. On Automorphism Groups of Countable Structures. J. Symbolic Logic, Tome 63 (1998) no. 1, pp.  891-896. http://gdmltest.u-ga.fr/item/1183745572/