English

$AD_{\mathbb{R}}$ implies that all sets of reals are $\Theta$ universally Baire

Logic 2021-10-13 v1

Abstract

ADRAD_{\mathbb{R}} is the Axiom of Determinacy for games on the reals (i.e., the player play reals. We show that it implies that all sets of reals are Theta-universally Baire. As a corollary we obtain a model in which ADAD holds and all sets of reals are fully universally Baire. Such a model was first constructed by Larson, Sargsyan and Wilson. Our result complements it as the technique is purely descriptive set theoretic.

Keywords

Cite

@article{arxiv.2110.06075,
  title  = {$AD_{\mathbb{R}}$ implies that all sets of reals are $\Theta$ universally Baire},
  author = {Grigor Sargsyan},
  journal= {arXiv preprint arXiv:2110.06075},
  year   = {2021}
}