黄片荔枝视频

Title: Extension properties and separability of groups: a connection between model theory and profinite topologies

Abstract: Hall's theorem states that free groups have an abundance of 'separable' subsets, i.e., sets which are closed in its profinite topology, and so free groups have strong decision properties. Strengthenings of this theorem have thus attracted much attention in geometric group theory, but naturally, these results are hard to come by. Notably, Ribes and Zalesski沫 proved that products of finitely generated subgroups of free groups are separable, settling a long-standing problem in finite monoid theory, and later, a breakthrough by Herwig and Lascar provided a formal equivalence between this theorem and extension properties of partial automorphisms of certain finite structures, which are of independent interest in model theory. In this talk, I will present Coulbois' generalization of the Herwig-Lascar equivalence to arbitrary groups, and also present a combinatorial proof of a generalization of the Ribes-Zalesski沫 theorem to other profinite topologies, due to Auinger and Steinberg, which is also in the spirit of extending partial automorphisms.

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