Projective measure without projective Baire
  We prove that it is consistent (relative to a Mahlo cardinal) that all projective sets of reals are Lebesgue measurable, but there is a $\Delta^1_3$ set without the Baire property. The complexity of the set which provides a counterexample to the Baire property is optimal. 
Sy Friedman and David Schrittesser
math.LO