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12.14 (1992)

Solved

If $T$ is a countable theory, does there exist a model $\mathcal{A}$ of $T$ such that the theory of $\text{Aut}(\mathcal{A})$ is undecidable?

Contributor: M. Giraudet, A. M.W. Glass

Progress

Yes, moreover, every first order theory having infinite models has a model whose automorphism group has undecidable existential theory (V. V. Bludov, M. Giraudet, A. M.W. Glass, G. Sabbagh, in Models, Modules and Abelian Groups, de Gruyter, Berlin, 2008, 325–328).

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