A new class of Ramsey-classification theorems and their applications in the Tukey theory of ultrafilters, Part 2
A new class of Ramsey-classification theorems and their applications in the Tukey theory of ultrafilters, Part 2
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一类新的 Ramsey 分类定理及其在超滤器 Tukey 理论中的应用，第 2 部分
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发表时间：
2012
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通讯作者：
S. Todorcevic
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作者：
Natasha Dobrinen;S. Todorcevic
受Tukey分类问题的启发，我们在这里开发了一个新的拓扑Ramsey空间R1，其复杂性仅次于经典的Ellentuck空间[8]。与R1相关联的是一个弱Ramsey但不是Ramsey的超滤子U1。我们证明了一个规范化定理的等价关系的前沿R1。这扩展了Pudlak-Rodl定理在Ellentuck空间上的障碍上的等价关系。然后，我们应用我们的标准化定理完全分类的所有Rudin-Keisler等价类的超滤是Tukey可约为U1：每一个超滤是Tukey可约为U1是同构于一个可数迭代的Fubini产品的超滤从一个固定的可数集合的超滤。此外，我们证明了严格低于U1的Tukey型非主超滤子，即Ramsey超滤子的Tukey型。
Motivated by a Tukey classification problem we develop here a new topological Ramsey space R1 that in its complexity comes immediately after the classical Ellentuck space [8]. Associated with R1 is an ultrafilter U1 which is weakly Ramsey but not Ramsey. We prove a canonization theorem for equivalence relations on fronts on R1. This extends the Pudlak-Rodl Theorem canonizing equivalence relations on barriers on the Ellentuck space. We then apply our canonization theorem to completely classify all Rudin-Keisler equivalence classes of ultrafilters which are Tukey reducible to U1: Every ultrafilter which is Tukey reducible to U1 is isomorphic to a countable iteration of Fubini products of ultrafilters from among a fixed countable collection of ultrafilters. Moreover, we show that there is exactly one Tukey type of nonprincipal ultrafilters strictly below that of U1, namely the Tukey type of a Ramsey ultrafilter.