# Sh:744

• Shelah, S. (2003). A countable structure does not have a free uncountable automorphism group. Bull. London Math. Soc., 35(1), 1–7.
• 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}
}