# Forcing and its Applications Retrospective Workshop, April 2015

I gave an invited talk at Forcing and its Applications Retrospective Workshop, Toronto, April 1st, 2015.

Title: A microscopic approach to Souslin trees constructions

Abstract: We present an approach to construct $\kappa$-Souslin trees that is insensitive to the identity of the cardinal $\kappa$, thereby, allowing to transform constructions from successor of regulars to successor of singulars and to inaccessibles. This is obtained by redirecting all constructions through a parametrized proxy principle.
The construction is carried as a transfinite sequence of microscopic steps that is indifferent of the “big picture”. Indeed, the features of the outcome tree are determined by the parameters of the proxy principle that one starts with.

This is joint work with Ari. M. Brodsky.