滤子二分原理不蕴含半滤子三分原理
The Filter Dichotomy Principle Does not Imply the Semifilter Trichotomy Principle
摘要：
我们肯定地回答了Blass在1989年提出的不等式$\gu < \gro$是否严格强于滤子二分法的问题。我们证明了存在一个力迫扩张，其中$ω$上的每个非稀疏滤子都是超有限对一的，并且半滤子剖分不成立。这个剖分说：每个半滤子要么是有限对一的贫乏的，要么是有限对一的，要么是有限对一的。该不等式等价于Blass和Laflamme的不等式$\gu<\gro$.块序列的组合学用于建立保持块序列的适当性质的力迫概念。
英文摘要：
We answer Blass' question from 1989 of whether the inequality $\gu < \gro$ is strictly stronger than the filter dichotomy principle affirmatively. We show that there is a forcing extension in which every non-meagre filter on $ω$ is ultra by finite-to-one and the semifilter trichotomy does not hold. This trichotomy says: every semifilter is either meagre or comeagre or ultra by finite-to-one. The trichotomy is equivalent to the inequality $\gu<\gro$ by work of Blass and Laflamme. Combinatorics of block sequences is used to establish forcing notions that preserve suitable properties of block sequences.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
