论文标题
较高kurepa树的描述性特性
Descriptive properties of higher Kurepa trees
论文作者
论文摘要
我们利用描述性集理论的概念的概括来研究无数正常基数的组合对象，专注于较高的kurepa树，并通过诸如功能空间的连续图像之类的树木来表示Cofinal分支的集合。对于不同类型的无数常规红衣主教$κ$，我们的结果为通过$κ$ -KUREPA树代表一组的所有一致场景提供了完整的图片，作为广义Baire Space $ {}^κκ$ $κ$的缩回。此外，这些结果可用于确定$ {}^κκ$连续图像的大多数相应陈述的一致性。
We use generalizations of concepts from descriptive set theory to study combinatorial objects of uncountable regular cardinality, focussing on higher Kurepa trees and the representation of the sets of cofinal branches through such trees as continuous images of function spaces. For different types of uncountable regular cardinals $κ$, our results provide a complete picture of all consistent scenarios for the representation of sets of cofinal branches through $κ$-Kurepa trees as retracts of the generalized Baire space ${}^κκ$ of $κ$. In addition, these results can be used to determine the consistency of most of the corresponding statements for continuous images of ${}^κκ$.
