### 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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