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arXiv · 1607.07033

More notions of forcing add a Souslin tree

Ari Meir Brodsky·Assaf Rinot
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Abstract

An $\aleph_1$-Souslin tree is a complicated combinatorial object whose existence cannot be decided on the grounds of ZFC alone. But 15 years after Tennenbaum and independently Jech 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 paper, we identify a rather large class of notions of forcing that, assuming a GCH-type assumption, add a $\lambda^+$-Souslin tree. This class includes Prikry, Magidor and Radin forcing.

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Ari Meir Brodsky, Assaf Rinot. 2016-07-24. More notions of forcing add a Souslin tree. https://doi.org/10.1215/00294527-2019-0011

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