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.
Bibliographical noteFunding Information:
This research was partially supported by the Israel Science Foundation (grant #1630/14).
© 2018 Canadian Mathematical Society.
- Souslin tree
- forcing axiom
- sharply dense set