A model with fragments of projective determinacy and failures of $\mathsf{DC}$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915298112700416 |
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| author | Müller, Sandra Wcisło, Bartosz |
| author_facet | Müller, Sandra Wcisło, Bartosz |
| contents | We describe a construction of a model of second order arithmetic in which (boldface) $\bm{Π^1_n}$-determinacy holds, but (lightface) $Π^1_{n+2}$-$\mathsf{DC}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16628 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A model with fragments of projective determinacy and failures of $\mathsf{DC}$ Müller, Sandra Wcisło, Bartosz Logic 03E45, 03E60, 03E30, 03E25, 03E35, 03F35 We describe a construction of a model of second order arithmetic in which (boldface) $\bm{Π^1_n}$-determinacy holds, but (lightface) $Π^1_{n+2}$-$\mathsf{DC}$ 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. |
| title | A model with fragments of projective determinacy and failures of $\mathsf{DC}$ |
| topic | Logic 03E45, 03E60, 03E30, 03E25, 03E35, 03F35 |
| url | https://arxiv.org/abs/2505.16628 |