Projective uniformization revisited Original Research Article

We give an optimal lower bound in terms of large cardinal axioms for the logical strength of projective uniformization (i.e., the assumption that for any projective set in the real plane there exists a projectively definable function selecting an element from each section of the given set) in conjuction with other regularity properties of projective sets of real numbers, namely Lebesgue measurability and its dual in the sense of category (the property of Baire). Our proof uses a projective computation of the real numbers which code inital segments of a core model and answers a question in Hauser (1995).