论文标题
超滤器在规范内部模型中的饱和特性
Saturation Properties of Ultrafilters in Canonical Inner Models
论文作者
论文摘要
我们改善了Galvin的Ultrafter的定理，这是P点的P点限制。这意味着，在所有规范的内部模型中，直至superstrong Casvinal，每个Kappa完整的超级滤波器上的可测量的红衣主教Kappa上都满足Galvin特性。另一方面，我们证明了超级紧张的红衣主教始终携带非加尔文kappa完全完整的超滤器。最后，我们证明了Diamond_kappa意味着存在Kappa-Complete过滤器，该过滤器扩展了俱乐部过滤器，并且无法满足Galvin属性。这回答了Gitik，Shelah，Garti和作者的问题。
We improve Galvin's Theorem for ultrafilters which are p-point limits of p-points. This implies that in all the canonical inner models up to a superstrong cardinal, every kappa-complete ultrafilter over a measurable cardinal kappa satisfies the Galvin property. On the other hand, we prove that supercompact cardinals always carry non-Galvin kappa-complete ultrafilters. Finally, we prove that diamond_kappa implies the existence of a kappa-complete filter which extends the club filter and fails to satisfy the Galvin property. This answers questions Gitik, Shelah, Garti and the author.
