A model with fragments of projective determinacy and failures of DC

2025/05/22 by Sandra Müller, Müller, Sandra, Bartosz Wcisło +1
Computer Science · Mathematics · #03E25 #03E30 #03E35 #03E45 #03E60 #03F35 #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2505.16628

openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a construction of a model of second order arithmetic in which (boldface) \bmΠ¹_n-determinacy holds, but (lightface) Π¹_n+2-DC fails, thus showing that no projective level of determinacy implies full DC_ℝ. The construction builds upon the work of Gitman, Friedman, and Kanovei.

Citations

• Mice with finitely many Woodin cardinals from optimal determinacy hypotheses
• A model of second-order arithmetic satisfying AC but not DC
• The definability of 𝔼 in self-iterable mice

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