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.

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2 Responses to More notions of forcing add a Souslin tree

  1. Pingback: Prikry forcing may add a Souslin tree | Assaf Rinot

  2. saf says:

    Submitted to Notre Dame Journal of Formal Logic, July 2016.
    Accepted, September 2017.

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