论文标题
链覆盖了没有无限抗的poset的数量
The chain covering number of a poset with no infinite antichains
论文作者
论文摘要
Poset $ P $的链条覆盖数$ \ cov（p）$是覆盖$ p $所需的链数。对于红衣主教$ν$，我们提供了一系列基数和覆盖数量$ν$的列表，以便对于每个poset $ p $，没有无限抗敌，$ \ cov（p）\ geq c n i时，仅当$ p $嵌入列表的成员时。如果$ν$是继任的红衣主教，即$ [ν]^2 $及其双重，则此列表具有两个元素，如果$ν$是$ \ cf（ν）$弱紧凑的限制性cardinal，则四个元素。对于$ν= \ aleph_1 $，第一作者给出了一个列表； F. Dorais将他的建筑扩展到每个无限的继任Cardinal $ν$。
The chain covering number $\Cov(P)$ of a poset $P$ is the least number of chains needed to cover $P$. For a cardinal $ν$, we give a list of posets of cardinality and covering number $ν$ such that for every poset $P$ with no infinite antichain, $\Cov(P)\geq ν$ if and only if $P$ embeds a member of the list. This list has two elements if $ν$ is a successor cardinal, namely $[ν]^2$ and its dual, and four elements if $ν$ is a limit cardinal with $\cf(ν)$ weakly compact. For $ν= \aleph_1$, a list was given by the first author; his construction was extended by F. Dorais to every infinite successor cardinal $ν$.
