论文标题
等效关系的拓扑拉西空间和可数列的双重拉姆西定理
Topological Ramsey spaces of equivalence relations and a dual Ramsey theorem for countable ordinals
论文作者
论文摘要
我们定义了由$ω$上的等价关系组成的拓扑拉西空间的集合，该属性是根据$ω$的固定分区而交替的，等价类的最小代表交替出现。为了证明相关的Pigonhole原理，我们利用了左侧的Hales-Jewett Theorem及其扩展到无限字母。我们还展示了如何将相应的无限维度拉姆西结果转移到可数极限序列上的等效关系（最多需要对等价类别的最小代表的必要限制），以便获得此类序数的双重ramsey定理。
We define a collection of topological Ramsey spaces consisting of equivalence relations on $ω$ with the property that the minimal representatives of the equivalence classes alternate according to a fixed partition of $ω$. To prove the associated pigeonhole principles, we make use of the left-variable Hales-Jewett theorem and its extension to an infinite alphabet. We also show how to transfer the corresponding infinite-dimensional Ramsey results to equivalence relations on countable limit ordinals (up to a necessary restriction on the set of minimal representatives of the equivalence classes) in order to obtain a dual Ramsey theorem for such ordinals.
