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Countable structure does not have a free uncountable automorphism group

Saharon Shelah
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Abstract

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 math.LO/0003120 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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Saharon Shelah. 2000-10-30. Countable structure does not have a free uncountable automorphism group. https://arxiv.org/abs/math/0010305

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