论文标题
无数的树木和Cohen $κ$ - 真实
Uncountable trees and Cohen $κ$-reals
论文作者
论文摘要
我们研究了一些在广义的康托尔和拜尔空间中的变形虫版本的树木燃料。这答案[10，问题3.20]，并概括了一系列研究，该研究已在[11]，[13]和[7]中研究了标准案例。此外，我们还回答了Friedman，Khomskii和Kulikov在[3]中提出的问题，内容涉及无数枢机主教处的规律性属性之间的关系。我们将$σ_1^1 $ -CounterExamples显示到与树木相关的一些规律性属性，而无需俱乐部分裂。特别是，我们证明了拉姆西和贝尔特性之间的牢固关系，与标准案例形成鲜明对比。
We investigate some versions of amoeba for tree-forcings in the generalized Cantor and Baire spaces. This answers [10, Question 3.20] and generalizes a line of research that in the standard case has been studied in [11], [13], and [7]. Moreover, we also answer questions posed in [3] by Friedman, Khomskii, and Kulikov, about the relationships between regularity properties at uncountable cardinals. We show $Σ_1^1$-counterexamples to some regularity properties related to trees without club splitting. In particular we prove a strong relationship between the Ramsey and the Baire properties, in slight contrast with the standard case.
