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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2506.23586 |
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- Generalizing the $ω$-categorical context, we introduce a notion, which we call the Lascar Property, that allows for a fine analysis of the topological isomorphisms between automorphism groups of countable structures satisfying this property. In particular, under the assumption of the Lascar Property, we exhibit a definable Galois correspondence between pointwise stabilizers of finitely generated Galois algebraically closed subsets of $M$ and finitely generated Galois algebraically closed subsets of $M$. We use this to characterize the group of automorphisms of $\mathrm{Aut}(M)$, for $M$ the countable saturated model of $\mathrm{ACF}_0$, $\mathrm{DCF}_0$, or the theory of infinite $\mathrm{K}$-vector spaces, generalizing results of Evans $\&$ Lascar, and Konnerth, while at the same time subsuming the analysis from [11] for $ω$-categorical structures with weak elimination of imaginaries.