A microscopic approach to Souslin-tree construction, Part II

Ari Meir Brodsky, Assaf Rinot

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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.

Original languageEnglish
Article number102904
JournalAnnals of Pure and Applied Logic
Volume172
Issue number5
DOIs
StatePublished - May 2021

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.

Keywords

  • Ascent path
  • Parameterized proxy principle
  • Postprocessing function
  • Souslin-tree construction
  • Streamlined trees
  • xbox

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