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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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Table of 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.