论文标题
您可以带走Komjath的无法访问吗？
Can You Take Komjath's Inaccessible Away?
论文作者
论文摘要
在本文中，我们旨在比较库雷帕树和aronszajn树。此外，我们分析了大型基本假设对此比较的影响。使用在序列上行走的方法，我们将表明它与ZFC一致，即有kurepa树，如果有一个无法访问的红衣主教，则每个kurepa树都包含一个Aronszajn子树。这比Komjath的定理强，该定理主张了两个无法访问的红衣主教的一致性。此外，我们证明与ZFC是一致的，有一个kurepa树$ t $，因此，如果$ u \ u \ subset t $是kurepa树，带有$ t $的遗传订单，则$ u $具有Aronszajn subtree。该定理不使用大型的基本假设。我们的最后一个定理立即表示以下内容：假设$ \ textrm {ma} _ {ω_2} $保持，$ω_2$不是$ \ textsc {l} $中的mahlo cardinal。然后是一棵kurepa树，每个kurepa子集都有一个aronszajn子树。我们的工作需要证明有关Todorcevic的$ρ$函数的新引理，这在其他情况下可能很有用。
In this paper we aim to compare Kurepa trees and Aronszajn trees. Moreover, we analyze the affect of large cardinal assumptions on this comparison. Using the the method of walks on ordinals, we will show it is consistent with ZFC that there is a Kurepa tree and every Kurepa tree contains an Aronszajn subtree, if there is an inaccessible cardinal. This is stronger than Komjath's theorem that asserts the same consistency from two inaccessible cardinals. Moreover, we prove it is consistent with ZFC that there is a Kurepa tree $T$ such that if $U \subset T$ is a Kurepa tree with the inherited order from $T$, then $U$ has an Aronszajn subtree. This theorem uses no large cardinal assumption. Our last theorem immediately implies the following: assume $\textrm{MA}_{ω_2}$ holds and $ω_2$ is not a Mahlo cardinal in $\textsc{L}$. Then there is a Kurepa tree with the property that every Kurepa subset has an Aronszajn subtree. Our work entails proving a new lemma about Todorcevic's $ρ$ function which might be useful in other contexts.
