More notions of forcing add a Souslin tree

Joint work with Ari Meir Brodsky.

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.

Downloads:

Citation information:

A. M. Brodsky and A. Rinot, More notions of forcing add a Souslin tree, Notre Dame J. Form. Log., 60(3): 437-455, 2019.