Group topologies on automorphism groups of homogeneous structures
Zaniar Ghadernezhad, Javier de la Nuez González
本文分类了可数自由齐性结构、Urysohn 空间与 Urysohn 球面自同构群上比有限集稳定子拓扑更粗的群拓扑，并得到相关结果。
我们分类了可数自由齐性结构、Urysohn 空间和 Urysohn 球面的自同构群中比有限集稳定子拓扑更粗的所有群拓扑，并给出了其他相关结果。
We classify all group topologies coarser than the topology of stabilizers of finite sets in the case of automorphism groups of countable free-homogeneous structures, Urysohn space and Urysohn sphere, among other related results.
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Topologies induced by group actions
本文引入拓扑群在群和环上作用诱导的典范拓扑，刻画了使作用连续的最细拓扑，并证明Polish群作用可能不存在Hausdorff拓扑。
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Every Polish group has a non-trivial topological group automorphism
本文证明每个具有超过两个元素的波兰群都存在非平凡的拓扑群自同构，并由此得出唯一同构的波兰空间无法成为半拓扑群的结论。
In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is concerned with Cameron's problem of classifying the homogeneous structures in a language of finitely many linear orders, which we call finite-dimensional permutation structures. Towards this problem, we present a construction that we conjecture produces all such structures. Some evidence for this conjecture is given, including the classification of the homogene…
We show that in algebraically locally finite countable homogeneous structures with a free stationary independence relation the small index property implies the strong small index property. We use this and the main result of [15] to deduce that countable free homogeneous structures in a locally finite relational language have the strong small index property. We also exhibit new continuum sized classes of $\aleph_0$-categorical structures with the strong small index property whose automorphism groups are pairwise non-isomorphic.
Homogeneous forcing
本文研究了保持序数幂并避免坍塌的迭代强迫，通过支持小于κ和κ⁺-cc条件，实现同质强迫以获得大量自同构。
Automorphism groups of prime models, and invariant measures
本研究将饱和模型下自同构群的可定义子集概念适配到原子强齐次模型的相对自同构群，探讨其可定义子集布尔代数上不变测度的存在唯一性（稳定理论下成立），并验证该可定义性与可定义伽罗瓦上同调、微分伽罗瓦理论的相容性。
Minimal and intrinsic topologies on monoids of elementary embeddings
研究单射嵌入空间的点wise收敛拓扑与代数 Zariski 拓扑的关系，探讨其在不同结构下的最小性及贡献。
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Generics in invariant subsets of some highly homogeneous permutation groups
本文证明不涉及循环序的闭高度齐次置换群中，共轭类闭包含余稠密共轭类，且有限部分映射族具共尾合并性质，并推广至典型超齐次偏序自同构。
Free groups are known to be homogeneous, meaning that finite tuples of elements which satisfy the same first-order properties are in the same orbit under the action of the automorphism group. We show that virtually free groups have a slightly weaker property, which we call uniform almost-homogeneity: the set of $k$-tuples which satisfy the same first-order properties as a given $k$-tuple $\mathbf{u}$ is the union of a finite number of $\mathrm{Aut}(G)$-orbits, and this number is bounded independently from $\mathbf{u}$ and $k$. Moreover, we prove that there exists a virtually free group which i…
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