Notre Dame Journal of Formal Logic

More Notions of Forcing Add a Souslin Tree

Ari Meir Brodsky and Assaf Rinot

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An 1-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 1-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.

Article information

Notre Dame J. Formal Logic, Volume 60, Number 3 (2019), 437-455.

Received: 18 July 2016
Accepted: 4 September 2017
First available in Project Euclid: 11 June 2019

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Mathematical Reviews number (MathSciNet)

Primary: 03E05: Other combinatorial set theory
Secondary: 03E35: Consistency and independence results 05C05: Trees 03E65: Other hypotheses and axioms

Souslin-tree construction microscopic approach Prikry forcing Magidor forcing Radin forcing Cohen forcing Hechler forcing parameterized proxy principle square principle outside guessing of clubs


Brodsky, Ari Meir; Rinot, Assaf. More Notions of Forcing Add a Souslin Tree. Notre Dame J. Formal Logic 60 (2019), no. 3, 437--455. doi:10.1215/00294527-2019-0011.

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