Reduced powers of Souslin trees

Joint work with Ari Meir Brodsky.

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 ${\mathrm{\aleph }}_6$-Souslin tree $T$ and a sequence of uniform ultrafilters $⟨{\mathcal{U}}_n\mid n<6⟩$ such that $T^{{\mathrm{\aleph }}_n}/{\mathcal{U}}_n$ is ${\mathrm{\aleph }}_6$-Aronszajn iff $n<6$ is not a prime number.

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Citation information:

A. M. Brodsky and A. Rinot, Reduced powers of Souslin trees, Forum Math. Sigma, 5(e2): 1-82, 2017.