论文标题
Souslin-Tree Construction的微观方法，第二部分
A microscopic approach to Souslin-tree construction, Part II
论文作者
论文摘要
在本系列的第一部分中，我们介绍了Souslin-Tree构造的微观方法，并认为所有已知的$ \ diamondsuit $基于$ \ diamondsuit $的构造具有各种其他属性，可以作为我们方法的应用渲染。在本文中，我们表明，即使在没有$ \ diamondsuit $的情况下，也可以执行相同方法的结构。特别是，我们为在难以接近的基数水平上存在苏斯林树的存在获得了新的弱条件。 我们还提出了带有上升路径的Souslin树的新结构，从而提高了从Mahlo Cardinal到弱紧凑的红衣主教的这种不存在的这种不存在的一致性强度。 本文的第2节针对具有最小背景的新移民。它提供了建造苏林树和所涉及的挑战的综合论述。
In Part I of this series, we presented the microscopic approach to Souslin-tree constructions, and argued that all known $\diamondsuit$-based constructions of Souslin trees with various additional properties may be rendered as applications of our approach. In this paper, we show that constructions following the same approach may be carried out even in the absence of $\diamondsuit$. In particular, we obtain a new weak sufficient condition for the existence of Souslin trees at the level of a strongly inaccessible cardinal. We also present a new construction of a Souslin tree with an ascent path, thereby increasing the consistency strength of such a tree's nonexistence from a Mahlo cardinal to a weakly compact cardinal. Section 2 of this paper is targeted at newcomers with minimal background. It offers a comprehensive exposition of the subject of constructing Souslin trees and the challenges involved.
