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 $\aleph_6$-Souslin tree $T$ and a sequence of uniform ultrafilters $\langle \mathcal U_n\mid n<6\rangle$ such that $ T^{\aleph_n}/\mathcal U_n$ is $\aleph_6$-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.

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Submitted to Forum of Mathematics, Sigma, July 2015.

Accepted, December 2016.