The consistency strength of projective uniformization, revisited
arXiv:math/9710201
Abstract
It is shown that if every projective set of reals is Lebesgue measurable and has the property of Baire, if every projective set in the plane has a projective uniformization, and if Steel's K exists, then J^K_{ω_1} \models "there are infinitely many strong cardinals." This is best possible, by a recent result of Steel.