Ramsey理论与0维流的拓扑动力学

中文摘要 AI 辅助

我们引入了0维ambit的几个Ramsey理论性质，并获得了它们的动力学刻画。因此，我们得到了所讨论ambit的一些重要不变量（特别是Ellis群）的平凡性和profinite性的Ramsey理论判据。这产生了每个给定的ambit的distal极小因子是profinite流这一结构性质的判据。另一个结果是Ellis半群中极小左理想的metrizability判据。然后，我们研究了上述抽象背景的三个特化：一阶理论、可定义群以及经典的Kechris-Pestov-Todorčević理论，在每个背景中恢复了已知结果并获得了新结果。

英文摘要

We introduce several Ramsey-theoretic properties of 0-dimensional ambits and obtain their dynamical characterizations. In consequence, we obtain Ramsey-theoretic criteria for triviality and for profiniteness of some important invariants (in particular, of the Ellis groups) of the ambits in question. This yields a criterion for the structural property that each distal minimal factor of the given ambit is a profinite flow. Another result is a criterion for metrizability of the minimal left ideals in the Ellis semigroup. Then we study three specializations of the above abstract context: to first order theories, to definable groups, and to the classical Kechris-Pestov-Todorčević theory, recovering known and obtaining new results in each of these contexts.

发表机构

• Instytut Matematyczny, Uniwersytet Wrocławski（弗罗茨瓦夫大学数学研究所）
• Department of Mathematics, Changwon National University（昌原国立大学数学系）
• University of Belgrade, Faculty of Mathematics（贝尔格莱德大学数学学院）

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