## Abstract

In this paper we study the determinacy strength of infinite games in the Cantor space and compare them with their counterparts in the Baire space. We show the following theorems: 1. RCA_{0} ⊢ Δ_{1} ^{0}* ↔ ∑_{1}^{0}-Det* ↔ WKL_{0}. 2. RCA_{0} ⊢ (∑_{1}^{0}) _{2}-Det* ↔ ACA_{0}. 3. RCA_{0} ⊢ Δ_{2}^{0}* ↔ ∑_{2} ^{0}-Det* ↔ Δ_{1}^{0}-Det ↔ ∑_{1}^{0}-Det ↔ ATR_{0}. 4. For 1 < k < w, RCA_{0} ⊢ (∑_{2}^{0})_{k}- Det* ↔ (∑_{2}^{0})_{k-1}-Det. 5. RCA _{0} ⊢ Δ_{3}^{0}* ↔ Δ_{3}^{0}-Det. Here, Det* (respectively Det) stands for the determinacy of infinite games in the Cantor space (respectively the Baire space), and (∑_{n}^{0})k is the collection of formulas built from ∑_{n}^{0} formulas by applying the difference operator k - 1 times.

Original language | English |
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Pages (from-to) | 226-236 |

Number of pages | 11 |

Journal | Mathematical Logic Quarterly |

Volume | 53 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2007 |

## Keywords

- Determinacy
- Reverse mathematics
- Second order arithmetic