论文标题
最大独立集，链/抗原理的变体和不含AC的Cofinal子集
Maximal independent sets, variants of chain/antichain principle and cofinal subsets without AC
论文作者
论文摘要
在没有选择公理（AC）的设定理论中，我们观察到以下陈述的新关系，其选择原理较弱。 1。每个本地有限的连接图都有一个最大独立集。 2。每个本地可数的连接图都有一个最大独立集。 3。如果在部分订购的集合中，所有抗细胞都是有限的，并且所有链都有$ \aleph_α$，则该集合的尺寸$ \aleph_α$如果$ \aleph_α$是常规的。 4。每个部分有序的集合都有一个由富有创始的子集。 5。如果$ g =（v_ {g}，e_ {g}）$是本地有限的和弦图，那么有一个$ <$ of $ v_ {g} $，以至于$ \ \ {w <v：\ {w，w，v，v \} \ in e_ {g} $ clique clique clique clique clique clique clique in clique in clique clique。
In set theory without the Axiom of Choice (AC), we observe new relations of the following statements with weak choice principles. 1. Every locally finite connected graph has a maximal independent set. 2. Every locally countable connected graph has a maximal independent set. 3. If in a partially ordered set all antichains are finite and all chains have size $\aleph_α$, then the set has size $\aleph_α$ if $\aleph_α$ is regular. 4. Every partially ordered set has a cofinal well-founded subset. 5. If $G=(V_{G},E_{G})$ is a connected locally finite chordal graph, then there is an ordering $<$ of $V_{G}$ such that $\{w < v : \{w,v\} \in E_{G}\}$ is a clique for each $v\in V_{G}$.
