Reduced powers of Souslin trees

What is the relationship between a Souslin tree and its reduced powers? and is there any difference between, say, the reduced w-power and the reduced w1-power of the same tree? In this talk, we shall present tools recently developed to answer these sort of questions. For instance, these tools allow to construct an w6-Souslin tree whose reduced w_n-power is Aronszajn iff n is not a prime number.

This is joint work with Ari Brodsky.