### Abstract

In this paper we develop a technique for proving determinacy of classes of the form ω^{2}-Π_{1} ^{1}+Γ (a refinement of the difference hierarchy on Π_{1} ^{1} lying between ω^{2}-Π_{1} ^{1} and (ω^{2}+1)-Π_{1} ^{1}) from weak principles, establishing upper bounds for the determinacy-strength of the classes ω^{2}-Π_{1} ^{1}+Σ_{α} ^{0} for all computable α and of ω^{2}-Π_{1} ^{1}+Δ^{1} _{1}. This bridges the gap between previously known hypotheses implying determinacy in this region.

Original language | English |
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Pages (from-to) | 83-115 |

Number of pages | 33 |

Journal | Annals of Pure and Applied Logic |

Volume | 169 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

### Keywords

- Descriptive set theory
- Determinacy

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## Cite this

Le Sueur, C. (2018). Determinacy of refinements to the difference hierarchy of co-analytic sets.

*Annals of Pure and Applied Logic*,*169*(1), 83-115. https://doi.org/10.1016/j.apal.2017.10.001