On this second talk I begin with Solovay's characterization of real-valued measurability in terms of generic elementary embeddings, and build on results of Judah to prove that if there is an atomlessly measurable cardinal, then all (boldface) Delta-1-3 sets of reals are Lebesgue measurable. This is optimal in two respects: Just from the existence of measurable cardinals we cannot prove that lightface Delta-1-3 sets are measurable, and there are models with atomlessly measurable cardinals where there is a non-measurable Sigma-1-3 set. I will also discuss some related results. Speaker(s): Andres Caicedo (Math Reviews)