English

Universally measurable sets may all be Delta^1_2

Logic 2023-06-21 v3

Abstract

We produce a forcing extension of the constructible universe \bL\bL in which every universally measurable set of reals is \uTDelta21\uTDelta^{1}_{2}, partially answering question CG from David Fremlin's problem list. The analogous result for category holds in the same model.

Keywords

Cite

@article{arxiv.2005.10399,
  title  = {Universally measurable sets may all be Delta^1_2},
  author = {Paul B. Larson and Saharon Shelah},
  journal= {arXiv preprint arXiv:2005.10399},
  year   = {2023}
}
R2 v1 2026-06-23T15:42:14.463Z