Reduced powers of Souslin trees

Abstract

We study the relationship between a $\kappa$-Souslin tree $T$ and its reduced powers $T^{\theta }/\mathcal{U}$. Previous works addressed this problem from the viewpoint of a single power $\theta$, whereas here, tools are developed for controlling different powers simultaneously. As a sample corollary, we obtain the consistency of an ${\aleph }_6$-Souslin tree $T$ and a sequence of uniform ultrafilters $⟨{\mathcal{U}}_n\mid n<6⟩$ such that $T^{{\aleph }_n}/{\mathcal{U}}_n$ is ${\aleph }_6$-Aronszajn iff $n<6$ is not a prime number.

Minor update to reflect changes to "Microscopic approach" paper on which this paper relies

References in corpus (2)

• A Microscopic approach to Souslin-tree constructions. Part I
• More notions of forcing add a Souslin tree

Cited by in corpus (3)

• Squares, ascent paths, and chain conditions
• More notions of forcing add a Souslin tree
• A forcing axiom deciding the generalized Souslin Hypothesis