  We apply the Dual Ramsey Theorem of Graham and Rothschild to prove the Ramsey
property for classes of finite Boolean algebras with distinguished ideals. This
allows us to compute the universal minimal flow of the group of automorphisms
of $\mathcal{P}(\omega_1)/\rm{fin},$ should it be isomorphic to
$\mathcal{P}(\omega)/\rm{fin}$ or not, and of other quotients of power set
algebras. Taking Fra\"iss\'e limits of these classes, we can compute universal
minimal flows of groups of homeomorphisms of the Cantor set fixing some closed
subsets.
