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

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.


03E05 Other combinatorial set theory
03E35 Consistency and independence results
05C05 Trees
03E65 Other set-theoretic hypotheses and axioms
Full Text: DOI arXiv Euclid


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