The Axiom of Real Determinacy and the Axiom of Real Blackwell Determinacy

2025/10/13 by Ikegami, Daisuke, Woodin, W. Hugh
#03E15 #03E60 #28A05 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2510.11034

Abstract

We show that the Axiom of Real Determinacy AD_ℝ and the Axiom of Real Blackwell Determinacy Bl-AD_ℝ are equivalent in ZF+DC. This answers the question of Löwe [15, Question 53]. While we do not know whether they are equivalent in ZF+AC_ω (ℝ), we show that the theories ZF+AD_ℝ and ZF+AC_ω (ℝ)+Bl-AD_ℝ are equiconsistent.

Citations

• Blackwell Games

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