Automorphism Groups of Countable Stable Structures

Gianluca Paolini; Saharon Shelah

Automorphism Groups of Countable Stable Structures

Logic 2018-11-20 v3

Authors: Gianluca Paolini , Saharon Shelah

Abstract

For every countable structure $M$ we construct an $\aleph_0$ -stable countable structure $N$ such that $Aut(M)$ and $Aut(N)$ 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 $Aut(M)$ .

Keywords

topological groups automorphism groups descriptive set theory

Cite

@article{arxiv.1712.02568,
  title  = {Automorphism Groups of Countable Stable Structures},
  author = {Gianluca Paolini and Saharon Shelah},
  journal= {arXiv preprint arXiv:1712.02568},
  year   = {2018}
}

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