Universally measurable sets may all be Delta^1_2

TL;DR

This paper constructs a model of set theory where all universally measurable sets of reals are at the level of elta^1_2, providing a partial answer to a longstanding question in descriptive set theory.

Contribution

It introduces a forcing extension of onstructible universe where universally measurable sets are elta^1_2, advancing understanding of their descriptive complexity.

Findings

All universally measurable sets are elta^1_2 in the constructed model

The same model ensures the analogous result for category

Provides a partial answer to a question in descriptive set theory

Abstract

We produce a forcing extension of the constructible universe $\bL$ in which every universally measurable set of reals is $\uTDelta^{1}_{2}$, partially answering question CG from David Fremlin's problem list. The analogous result for category holds in the same model.