AD_\ℝ implies that all sets of reals are \Θ\n universally Baire

2021/10/12 by Grigor Sargsyan, Sargsyan, Grigor
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #Computability, Logic, AI Algorithms #Decision-Making and Behavioral Economics #Economic theories and models #FOS: Mathematics #Game Theory and Applications #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2110.06075

openalex publication_date 2021/10/12 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

AD_\ℝ is the Axiom of Determinacy for games on the reals (i.e.,\nthe player play reals. We show that it implies that all sets of reals are\nTheta-universally Baire. As a corollary we obtain a model in which AD holds\nand all sets of reals are fully universally Baire. Such a model was first\nconstructed by Larson, Sargsyan and Wilson. Our result complements it as the\ntechnique is purely descriptive set theoretic.\n

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