Countable structure does not have a free uncountable automorphism group

Details Countable structure does not have a free uncountable automorphism group Countable structure does not have a free uncountable automorphism group

2000-10-30

arxiv.org/abs/math/0010305v1

Mathematics

Logic

Scientific paper

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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