A forcing axiom deciding the generalized Souslin Hypothesis

Abstract

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 $\lambda$, if ${\lambda }^{++}$ is not a Mahlo cardinal in Gödel's constructible universe, then $2^{\lambda }={\lambda }^{+}$ entails the existence of a ${\lambda }^{+}$-complete ${\lambda }^{++}$-Souslin tree.

References in corpus (4)

• A microscopic approach to Souslin-tree construction, Part II
• A Microscopic approach to Souslin-tree constructions. Part I
• Distributive Aronszajn trees
• Reduced powers of Souslin trees

Cited by in corpus (1)

• Are all natural numbers the same