More Notions of Forcing Add a Souslin Tree

Notre Dame Journal of Formal Logic 60 (3):437-455 (2019)
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Abstract

An ℵ1-Souslin tree is a complicated combinatorial object whose existence cannot be decided on the grounds of ZFC alone. But fifteen years after Tennenbaum and Jech independently devised notions of forcing for introducing such a tree, Shelah proved that already the simplest forcing notion—Cohen forcing—adds an ℵ1-Souslin tree.In this article, we identify a rather large class of notions of forcing that, assuming a GCH-type hypothesis, add a λ+-Souslin tree. This class includes Prikry, Magidor, and Radin forcing.

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Citations of this work

A Microscopic Approach to Souslin-Tree Construction, Part II.Ari Meir Brodsky & Assaf Rinot - 2021 - Annals of Pure and Applied Logic 172 (5):102904.
Souslin Trees at Successors of Regular Cardinals.Assaf Rinot - 2019 - Mathematical Logic Quarterly 65 (2):200-204.

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References found in this work

Squares, Scales and Stationary Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
Scales, Squares and Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (1):35-98.
Forcing Closed Unbounded Sets.Uri Abraham & Saharon Shelah - 1983 - Journal of Symbolic Logic 48 (3):643-657.
The Fine Structure of the Constructible Hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
Aronszajn Trees, Square Principles, and Stationary Reflection.Chris Lambie-Hanson - 2017 - Mathematical Logic Quarterly 63 (3-4):265-281.

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