We will discuss a conjecture of Lionel Nguyen van Th\'e as
in the title. It was shown by Andy Zucker to be equivalent to whether
every class of finitary approximations of a countable ultrahomogeneous
structure with oligomorphic automorphism group has a finite Ramsey
degree. We look at the problem from the Boolean algebra point of view.
An interesting example in this context is the automorphism group of a
topological structure whose natural quotient is the pseudo-arc, which
is a work in progress with Aleksandra Kwiatkowksa (UCLA).