论文标题
本地O最低结构中的可定义商
Definable quotients in locally o-minimal structures
论文作者
论文摘要
令$ \ mathcal f =（f， +。\ cdot，<，0，1，\ dots）$是订购字段的本地o-minimal扩展。当满足几个技术条件时，我们证明了可确定的等价关系的可定义集合的存在。当$ x $是$ f^n $的本地可定义子集时，这些条件会得到满足，并且在$ x $上有可确定的组$ g $的可确定措施。
Let $\mathcal F=(F, +. \cdot, <, 0, 1, \dots)$ be a definably complete locally o-minimal expansion of an ordered field. We demonstrate the existence of definable quotients of definable sets by definable equivalence relations when several technical conditions are satisfied. These conditions are satisfied when $X$ is a locally closed definable subset of $F^n$ and there is a definable proper action of a definable group $G$ on $X$.
