Projective measure without projective Baire

Abstract

We prove that it is consistent (relative to a Mahlo cardinal) that all projective sets of reals are Lebesgue measurable, but there is a ${\Delta }_3^1$ set without the Baire property. The complexity of the set which provides a counterexample to the Baire property is optimal.

References in corpus (1)

• Coding over Core Models

Cited by in corpus (3)

• Coding over Core Models
• On the sepration of regularity properties of the reals
• Forcing the ${\Pi }_3^1$-Reduction Property and a Failure of ${\Pi }_3^1$-Uniformization