Projective Measure Without Projective Baire

The authors 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 David Friedman, Kurt Godel Research Center, University of Vienna, Austria. David Schrittesser, Kurt Godel Research Center, University of Vienna, Austria