A Forcing Axiom Deciding the Generalized Souslin Hypothesis

Chris Lambie-Hanson, Assaf Rinot

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We derive a forcing axiom from the conjunction of square and diamond, and present a few applications, primary among them being the existence of super-Souslin trees. It follows that for every uncountable cardinal λ, if λ ++ is not a Mahlo cardinal in Gödel's constructible universe, then 2 λ = λ + entails the existence of a λ + -complete λ ++ -Souslin tree.

Original languageEnglish
Pages (from-to)437-470
Number of pages34
JournalCanadian Journal of Mathematics
Issue number2
StatePublished - 1 Apr 2019

Bibliographical note

Funding Information:
This research was partially supported by the Israel Science Foundation (grant #1630/14).

Publisher Copyright:
© 2018 Canadian Mathematical Society.


  • SDFA
  • Souslin tree
  • diamond
  • forcing axiom
  • sharply dense set
  • square


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