Automorphism groups of countable stable structures
Volume 248 / 2020
Fundamenta Mathematicae 248 (2020), 301-307
MSC: 03C45, 03E15, 22F50.
DOI: 10.4064/fm723-4-2019
Published online: 6 September 2019
Abstract
For every countable structure $M$ we construct an $\aleph _0$-stable countable structure $N$ such that $\operatorname{Aut} (M)$ and $\operatorname{Aut} (N)$ are topologically isomorphic. This shows that it is impossible to detect any form of stability of a countable structure $M$ from the topological properties of the Polish group $\operatorname{Aut} (M)$.
