A microscopic approach to Souslin-tree construction, Part II

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

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.

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Citations of this work

On the ideal J[κ].Assaf Rinot - 2022 - Annals of Pure and Applied Logic 173 (2):103055.
Knaster and Friends III: Subadditive Colorings.Chris Lambie-Hanson & Assaf Rinot - 2023 - Journal of Symbolic Logic 88 (3):1230-1280.

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