Abstract
Suppose every (definable) set of real numbers has the Ramsey property and (definable) relations on the real numbers can be uniformized by a function on a set which is comeager in the Ellentuck topology. Then there are no (definable) MAD families. As it turns out, there are also no (fin x fin)-MAD families, where fin x fin is the two-dimensional Fubini product of the ideal of finite sets. We also comment on work in progress regarding higher dimensional products. All results are joint work with Asger Törnquist.