  Set disjointness is a central problem in communication complexity. Here Alice
and Bob each receive a subset of an n-element universe, and they need to decide
whether their inputs intersect or not. The communication complexity of this
problem is relatively well understood, and in most models, including $-$ most
famously $-$ interactive randomised communication with bounded error, the
problem requires much communication.
  In this work we were looking for a variation of the set disjointness problem,
as natural and simple as possible, for which the known lower bound methods
would fail, and thus a new approach would be required in order to understand
its complexity. The problem that we have found is a relational one: each player
receives a subset as input, and the goal is to find an element that belongs to
both players. We call it inevitable intersection.
