In recent joint work with Asger Toernquist, we showed how to construct 
definable maximal discrete sets in forcing extensions of L,
in particular in the Sacks and Miller extension. In particular, the 
existence of such sets is consistent with V \neq L.

In this talk I shall show the stronger result that the existence of 
definable discrete sets is consistent with large continuum. In the 
process, I show an interesting generalization of Galvin's theorem. In 
particular, this applies
to the example of maximal orthogonal families of measures (mofs).

One might hope for a simpler way of constructing a mof in a model with 
large continuum: to find an indestructible such family in L. While such 
an approach is possible e.g. for maximal cofinitary groups, this is 
impossible for mofs.