More notions of forcing add a souslin tree

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 λ⁺ C-Souslin tree. This class includes Prikry, Magidor, and Radin forcing.