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Brodsky, Ari Meir; Rinot, Assaf

More notions of forcing add a Souslin tree. (English) Zbl 07120749

Notre Dame J. Formal Logic 60, No. 3, 437-455 (2019).
Summary: An \(\aleph_1\)-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 \(\aleph_1\)-Souslin tree.
In this article, we identify a rather large class of notions of forcing that, assuming a GCH-type hypothesis, add a \(\lambda^+\)-Souslin tree. This class includes Prikry, Magidor, and Radin forcing.

Cited in 6 Documents

MSC:

03E05 Other combinatorial set theory
03E35 Consistency and independence results
05C05 Trees
03E65 Other set-theoretic hypotheses and axioms

Keywords:

Souslin-tree construction; microscopic approach; Prikry forcing; Magidor forcing; Radin forcing; Cohen forcing; Hechler forcing; parameterized proxy principle; square principle; outside guessing of clubs
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\textit{A. M. Brodsky} and \textit{A. Rinot}, Notre Dame J. Formal Logic 60, No. 3, 437--455 (2019; Zbl 07120749)
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References:

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