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

Grigor Sargsyan

paper

$A D_{R}$ implies that all sets of reals are $Θ$ universally Baire

arXiv:2110.06075

Abstract

$A D_{R}$ 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 $A D$ 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.

ADR​ implies that all sets of reals are Θ universally Baire

Abstract

$A D_{R}$ implies that all sets of reals are $Θ$ universally Baire