The determined Property of Baire in Reverse Math

@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}
}
  • Eric P. Astor, Damir D. Dzhafarov, +2 authors L. Westrick
  • Published 2020
  • Mathematics, Computer Science
  • J. Symb. Log.
  • 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
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