Countable structure does not have a free uncountable automorphism group

2000/10/30 by Saharon Shelah, Shelah, Saharon
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO

paper · pdf · doi:10.48550/arxiv.math/0010305

published as Bull. London Math. Soc. 35 No. 1 (2003) 1--7

arxiv created 2000/10/30 · arxiv updated 2009/11/30

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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