# Sh:1178

• Larson, P. B., & Shelah, S. Universally measurable sets may all be \boldsymbol{\Delta}^{1}_{2}. Preprint. arXiv: 2005.10399
• Abstract:
We produce a forcing extension of the constructible universe \bf L in which every sufficiently regular subset of any Polish space is a continuous image of a coanalytic set. In particular, we show that consistently every universally measurable set is \Delta^{1}_{2}, partially answering question CG from David Fremlin’s problem list [FQL].
• Version 2020-05-07 (19p)
Bib entry
@article{Sh:1178,
author = {Larson, Paul B. and Shelah, Saharon},
title = {{Universally measurable sets may all be $\boldsymbol{\Delta}^{1}_{2}$}},
note = {\href{https://arxiv.org/abs/2005.10399}{arXiv: 2005.10399}},
arxiv_number = {2005.10399}
}