We isolate two abstract determinacy theorems for games of length $\omega_1$ from work of Neeman and use them to conclude, from large-cardinal assumptions and an iterability hypothesis in the region of measurable Woodin cardinals that(1)if the Continuum Hypothesis holds, then all games of length $\omega_1$ which are provably $\Delta_1$ -definable from a universally Baire parameter (in first-order or $\Omega $ -logic) are determined;(2)all games of length $\omega_1$ with payoff constructible relative to the play are determined; and(3)if the Continuum Hypothesis holds, then there is a model of ${\mathsf{ZFC}}$ containing all reals in which all games of length $\omega_1$ definable from real and ordinal parameters are determined.

中文翻译：

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可证明的游戏

我们分离出长度游戏的两个抽象确定性定理$\omega_1$根据尼曼的工作并使用它们得出结论，根据大基数假设和可测量伍丁基数区域中的可迭代性假设，(1)如果连续统假设成立，那么所有长度游戏$\omega_1$这是可证明的$\Delta_1$- 可从通用的 Baire 参数定义（一阶或$\欧米茄$-逻辑）被确定；(2)所有长度的游戏$\omega_1$确定与游戏相关的可构造收益；和(3)如果连续统假设成立，那么有一个模型${\mathsf{ZFC}}$包含所有实数，其中所有长度的游戏$\omega_1$可从实数和序数参数确定。