论文标题
波兰太空分区原则和Halpern-Läuchli定理
Polish space partition principles and the Halpern-Läuchli theorem
论文作者
论文摘要
Halpern-Läuchli定理是树木的组合结果，由于Harrington使用强迫的想法而承认了优雅的证明。为了提炼此证明的组合本质，我们隔离了有关完美波兰空间产品的各种分区原则。这些原则产生了Halpern-Läuchli定理的直接证明，而哈灵顿证明的强迫也可以迫使它们的一致性。我们还表明，这些原理不是ZFC定理，表明它们在连续体的大小上放置了下限。
The Halpern-Läuchli theorem, a combinatorial result about trees, admits an elegant proof due to Harrington using ideas from forcing. In an attempt to distill the combinatorial essence of this proof, we isolate various partition principles about products of perfect Polish spaces. These principles yield straightforward proofs of the Halpern-Läuchli theorem, and the same forcing from Harrington's proof can force their consistency. We also show that these principles are not ZFC theorems by showing that they put lower bounds on the size of the continuum.
