论文标题
等价关系和决定性
Equivalence Relations and Determinacy
论文作者
论文摘要
我们介绍了$（γ，e）$的概念 - $γ$ a PointClass的确定性和波兰空间$ x $的等价关系的$γ$。当$ e = e_g $是$ s^g $上的$ g $的（左）移动$ s = 2 = 2 = \ {0,1 \} $或$ s =ω$时。我们表明，对于可数组$ g $的所有轮班动作，以及任何“合理的”点级$γ$，$（γ，e_g）$ - 确定性意味着$γ$ - 确定性。当$ e $是$ 2^\ mathbb {z} $的有限类型的Shift Map的子缩影时，我们还证明了相应的结果。
We introduce the notion of $(Γ,E)$-determinacy for $Γ$ a pointclass and $E$ an equivalence relation on a Polish space $X$. A case of particular interest is the case when $E=E_G$ is the (left) shift-action of $G$ on $S^G$ where $S=2=\{0,1\}$ or $S=ω$. We show that for all shift actions by countable groups $G$, and any "reasonable" pointclass $Γ$, that $(Γ,E_G)$-determinacy implies $Γ$-determinacy. We also prove a corresponding result when $E$ is a subshift of finite type of the shift map on $2^\mathbb{Z}$.
