Annals of Pure and Applied Logic 172 (5):102904 (2021)

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.
Keywords Souslin-tree construction  Parameterized proxy principle  xbox  Postprocessing function  Ascent path  Streamlined trees
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DOI 10.1016/j.apal.2020.102904
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References found in this work BETA

Set Theory: An Introduction to Large Cardinals.F. R. Drake & T. J. Jech - 1976 - British Journal for the Philosophy of Science 27 (2):187-191.
Some Exact Equiconsistency Results in Set Theory.Leo Harrington & Saharon Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (2):178-188.
Constructibility.Keith J. Devlin - 1987 - Journal of Symbolic Logic 52 (3):864-867.
Introduction to Set Theory.K. Hrbacek & T. Jech - 2001 - Studia Logica 69 (3):448-449.
The Fine Structure of the Constructible Hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.

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Citations of this work BETA

On the Ideal J[Κ].Assaf Rinot - 2022 - Annals of Pure and Applied Logic 173 (2):103055.

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