Mitchell序中的无穷减链
Infinite decreasing chains in the Mitchell order
摘要：
众所周知，米切尔秩序的行为在等级到等级扩展者的水平上发生了重大变化，因为它不再是有根据的。虽然在秩到秩扩展子之下的米切尔序的可能偏序结构被认为是很好理解的，但对缺乏根据的情况下的结构知之甚少。本文的目的是通过研究米切尔命令在多大程度上是站不住脚的，从而迈出理解这一案例的第一步。我们的主要结果是：（i）在秩到秩扩张子存在的情况下，存在任意可数长度的扩张子的传递Mitchell降序序列;（ii）不存在这样的长度为$ω_1$的序列.
英文摘要：
It is known that the behavior of the Mitchell order substantially changes at the level of rank-to-rank extenders, as it ceases to be well-founded. While the possible partial order structure of the Mitchell order below rank-to-rank extenders is considered to be well understood, little is known about the structure in the ill-founded case. The purpose of the paper is to make a first step in understanding this case, by studying the extent to which the Mitchell order can be ill-founded. Our main results are (i) in the presence of a rank-to-rank extender there is a transitive Mitchell order decreasing sequence of extenders of any countable length, and (ii) there is no such sequence of length $ω_1$.
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。
