Determinacy in L(R,μ)

2012/01/29 by Nam Trang, Trang, Nam
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Mathematical Analysis and Transform Methods #math.LO

paper · pdf · doi:10.48550/arxiv.1201.6005

openalex publication_date 2012/01/29 · arxiv created 2013/09/01 · arxiv updated 2013/09/03 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

Assume L(ℝ,μ) satisfies ZF+DC+Θ>ω₂ + μis a normal fine measure on \powerset_ω1(ℝ). The main result of this paper is the characterization theorem of L(ℝ,μ) which states that L(ℝ,μ) satisfies Θ>ω₂ if and only if L(ℝ,μ) satisfies AD⁺. As a result, we obtain the equiconsistency between the two theories: "ZFC + there are ω² Woodin cardinals" and "ZF+DC+μis a normal fine measure on \powerset_ω1(ℝ) + Θ>ω₂".

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