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An « Ahlbrandt-Ziegler Reconstruction » for theories which are not necessarily countably categorical Ben Yaacov, Itaï


It is by now almost folklore that if T is a countably categorical theory, and M its unique countable model, then the topological group G(T) = Aut(M) is a complete invariant for the bi-interpretability class of T . This gained renewed interest recently, given the correspondences between dynamical properties of G(T) and classification-theoretic properties of T . From a model-theoretic point of view, the obvious drawback is the restriction to countably categorical theories. As a first step, I will discuss how to generalise the original result to arbitrary theories in a countable language.

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