The Limits of Determinacy in Higher-Order Arithmetic
Logic
2024-11-08 v1
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.
Keywords
Cite
@article{arxiv.2411.04786,
title = {The Limits of Determinacy in Higher-Order Arithmetic},
author = {Juan Pablo Aguilera and Thibaut Kouptchinsky},
journal= {arXiv preprint arXiv:2411.04786},
year = {2024}
}