More notions of forcing add a souslin tree

Ari Meir Brodsky, Assaf Rinot

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)437-455
Number of pages19
JournalNotre Dame Journal of Formal Logic
Volume60
Issue number3
DOIs
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© 2019 by University of Notre Dame.

Keywords

  • Cohen forcing
  • Hechler forcing
  • Magidor forcing
  • Microscopic approach
  • Outside guessing of clubs
  • Parameterized proxy principle
  • Prikry forcing
  • Radin forcing
  • Souslin-tree construction
  • square principle

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