In Part I of this series, we presented the microscopic approach to Souslin-tree constructions, and argued that all known ⋄-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 ⋄. 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.

在本系列的第一部分中，我们介绍了苏斯林树构造的微观方法，并认为所有已知的基于⋄的苏斯林树具有各种其他属性的构造都可以作为我们方法的应用。在本文中，我们表明即使没有⋄，也可以执行遵循相同方法的构造。尤其是，我们获得了在极难接近的基数水平上存在苏斯林树的新的弱充分条件。

我们还提出了一种具有上升路径的Souslin树的新构造，从而增加了从Mahlo红衣主教到弱致密红衣主教这种树不存在的一致性强度。

本文的第2节针对背景最少的新手。它提供了有关构建苏斯林树的主题以及所涉及挑战的全面论述。