Universally measurable sets may all be $\mathop{\Delta}\limits_\sim {}^{1}_{2}$
Volume 266 / 2024
Fundamenta Mathematicae 266 (2024), 97-120
MSC: Primary 03E35; Secondary 28A20
DOI: 10.4064/fm318-3-2024
Published online: 4 July 2024
Abstract
We produce a forcing extension of the constructible universe $\mathbf L$ in which every universally measurable set of reals is $\mathop{\Delta}\limits_\sim {}^{1}_{2}$, partially answering question CG from David Fremlin’s problem list. The analogous result for category holds in the same model.
