2024/11/07 by Juan P. Aguilera, Aguilera, Juan Pablo, Thibaut Kouptchinsky +1
Computer Science · #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2411.04786
openalex publication_date 2024/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.