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arXiv · 2505.16628

A model with fragments of projective determinacy and failures of $\mathsf{DC}$

Sandra Müller·Bartosz Wcisło
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Abstract

We describe a construction of a model of second order arithmetic in which (boldface) $\bm{\Pi^1_n}$-determinacy holds, but (lightface) $\Pi^1_{n+2}$-$\mathsf{DC}$ fails, thus showing that no projective level of determinacy implies full $\mathsf{DC}_{\mathbb{R}}$. The construction builds upon the work of Gitman, Friedman, and Kanovei.

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Sandra Müller, Bartosz Wcisło. 2025-05-22. A model with fragments of projective determinacy and failures of $\mathsf{DC}$. https://arxiv.org/abs/2505.16628

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