More notions of forcing add a Souslin tree

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.

15 pages. Submitted

References in corpus (2)

• A Microscopic approach to Souslin-tree constructions. Part I
• Reduced powers of Souslin trees

Cited by in corpus (3)

• A microscopic approach to Souslin-tree construction, Part II
• Reduced powers of Souslin trees
• The power of trees