论文标题
虚构的标准
A criterion for uniform finiteness in the imaginary sorts
论文作者
论文摘要
让$ t $成为一种理论。如果$ t $消除$ \ cestists^\ infty $，则不必遵循$ t^{eq} $消除$ \ evenest^\ infty $，如$ p $ - ad的示例所示。我们给出一个标准，以确定$ t^{eq} $是否消除了$ \ conists^\ infty $。具体来说，我们表明$ t^{eq} $消除了$ \存在^\ infty $，并且仅当所有可解释的“非信念”集中消除了$ \ insists^\ infty $。可以在未知的$ t^{eq} $的完整描述的情况下应用此标准。作为一个应用程序，我们表明$ t^{eq} $消除了$ \的存在^\ infty $当$ t $是ACVF的c-Minimal扩展时。
Let $T$ be a theory. If $T$ eliminates $\exists^\infty$, it need not follow that $T^{eq}$ eliminates $\exists^\infty$, as shown by the example of the $p$-adics. We give a criterion to determine whether $T^{eq}$ eliminates $\exists^\infty$. Specifically, we show that $T^{eq}$ eliminates $\exists^\infty$ if and only if $\exists^\infty$ is eliminated on all interpretable sets of "unary imaginaries." This criterion can be applied in cases where a full description of $T^{eq}$ is unknown. As an application, we show that $T^{eq}$ eliminates $\exists^\infty$ when $T$ is a C-minimal expansion of ACVF.
