  We prove, using only weak choice principles, that if every set of reals has
the Ramsey Property, then there are no infinite maximal almost disjoint
families with respect to the transfinitely iterated Fr\'{e}chet ideals. These
results were announced by the authors in the Proceedings of the National
Academy of Sciences of the U.S.A.
  Complementing the above, we also show that the same conclusion cannot be
obtained in the pointclass $\Sigma^1_2$ if the Ramsey Property is replaced by
the assumption that all $\Sigma^1_2$ sets are Laver measurable.
