@article{Astor2020TheDP,
title={The determined Property of Baire in Reverse Math},
author={Eric P. Astor and Damir D. Dzhafarov and A. Montalb{\'a}n and R. Solomon and L. Westrick},
journal={J. Symb. Log.},
year={2020},
volume={85},
pages={166-198}
}

We define the notion of a determined Borel code in reverse math, and consider the principle $DPB$, which states that every determined Borel set has the property of Baire. We show that this principle is strictly weaker than $ATR$. Any $\omega$-model of $DPB$ must be closed under hyperarithmetic reduction, but $DPB$ is not a theory of hyperarithmetic analysis. We show that whenever $M\subseteq 2^\omega$ is the second-order part of an $\omega$-model of $DPB$, then for every $Z \in M$, there is a… CONTINUE READING