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arXiv · 2411.04786

The Limits of Determinacy in Higher-Order Arithmetic

Juan Pablo Aguilera·Thibaut Kouptchinsky
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Abstract

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 Montalb\'an-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.

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Juan Pablo Aguilera, Thibaut Kouptchinsky. 2024-11-07. The Limits of Determinacy in Higher-Order Arithmetic. https://arxiv.org/abs/2411.04786

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