Automorphism Groups of Countable Stable Structures
Gianluca Paolini, Saharon Shelah

TL;DR
The paper constructs a stable structure with an automorphism group topologically isomorphic to that of any given countable structure, demonstrating stability cannot be inferred from the automorphism group's topology.
Contribution
It introduces a method to associate a stable structure to any countable structure with an isomorphic automorphism group, highlighting limitations in detecting stability via automorphism groups.
Findings
Automorphism groups of countable structures can be topologically isomorphic regardless of stability.
Stability of a structure is not reflected in the topological properties of its automorphism group.
The construction applies to all countable structures, showing a fundamental limitation in model-theoretic classification.
Abstract
For every countable structure we construct an -stable countable structure such that and are topologically isomorphic. This shows that it is impossible to detect any form of stability of a countable structure from the topological properties of the Polish group .
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