A countable structure does not have a free uncountable automorphism group

by Shelah. [Sh:744]
Bulletin London Math Soc, 2003
Solecki proved that the group of automorphisms of a countable structure cannot be an uncountable free abelian group. See more in Just, Shelah and Thomas [JShT:654] where as a by product we can say something on on uncountable structures. We prove here the following Theorem: If A is a countable model, then Aut (M) cannot be a free uncountable group.


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