Submission date: 4 January 2007

Abstract:

Results are obtained on the question: if two omega-categorical structures have automorphism groups which are isomorphic as abstract groups, are the structures bi-interpretable? (In full generality, the answer is known to be negative.) The methods combine an approach of Rubin, comeagre conjugacy classes, and results of Hrushovski and Herwig on extending partial isomorphisms.

Mathematics Subject Classification: 03C35, 20B07

Keywords and phrases: homogeneous structure, reconstruction from automorphism group, omega-categoricity

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