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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.04786 |
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| _version_ | 1866917830426886144 |
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| author | Aguilera, Juan Pablo Kouptchinsky, Thibaut |
| author_facet | Aguilera, Juan Pablo Kouptchinsky, Thibaut |
| contents | We prove level-by-level upper and lower bounds on the strength of determinacy for finite differences of sets in the hyperarithmetical hierarchy in terms of subsystems of finite-and transfinite-order arithmetic, extending the Montalbán-Shore theorem to each of the levels of the Borel hierarchy beyond the one they treated. We also prove equivalences between reflection principles for higher-order arithmetic and quantified determinacy axioms, answering two questions of Pacheco and Yokoyama. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04786 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Limits of Determinacy in Higher-Order Arithmetic Aguilera, Juan Pablo Kouptchinsky, Thibaut Logic We prove level-by-level upper and lower bounds on the strength of determinacy for finite differences of sets in the hyperarithmetical hierarchy in terms of subsystems of finite-and transfinite-order arithmetic, extending the Montalbán-Shore theorem to each of the levels of the Borel hierarchy beyond the one they treated. We also prove equivalences between reflection principles for higher-order arithmetic and quantified determinacy axioms, answering two questions of Pacheco and Yokoyama. |
| title | The Limits of Determinacy in Higher-Order Arithmetic |
| topic | Logic |
| url | https://arxiv.org/abs/2411.04786 |