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

Grigor Sargsyan

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arXiv · 2110.06075

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

Grigor Sargsyan

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Abstract

$AD_{\mathbb{R}}$ 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 $AD$ 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.

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BibTeX RIS

Grigor Sargsyan. 2021-10-12. $AD_{\mathbb{R}}$ implies that all sets of reals are $\Theta$ universally Baire. https://arxiv.org/abs/2110.06075

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