# Sh:744

- Shelah, S. (2003).
*A countable structure does not have a free uncountable automorphism group*. Bull. London Math. Soc.,**35**(1), 1–7. arXiv: math/0010305 DOI: 10.1112/S0024609302001534 MR: 1934424 -
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 [JShT:654] where as a by product we can say something on on uncountable structures. We prove here the following Theorem: If {\mathbb A} is a countable model, then {\rm Aut}(M) cannot be a free uncountable group. - published version (7p)

Bib entry

@article{Sh:744, author = {Shelah, Saharon}, title = {{A countable structure does not have a free uncountable automorphism group}}, journal = {Bull. London Math. Soc.}, fjournal = {The Bulletin of the London Mathematical Society}, volume = {35}, number = {1}, year = {2003}, pages = {1--7}, issn = {0024-6093}, doi = {10.1112/S0024609302001534}, mrclass = {20B27 (03C60 03E15 20A15)}, mrnumber = {1934424}, mrreviewer = {Johannes Siemons}, doi = {10.1112/S0024609302001534}, note = {\href{https://arxiv.org/abs/math/0010305}{arXiv: math/0010305}}, arxiv_number = {math/0010305} }