论文标题
结构定理用于实际添加剂组的i最小扩展
Structure theorem for i-minimal expansions of the real additive ordered group
论文作者
论文摘要
We prove that for an o-minimal expansion of the real additive group $\cal R$ and a set $P\subseteq \mathbb{R}$ of dimension $0$ such that $\langle\mathcal{R},P\rangle$ is sparse, has definable choice and every definable set has interior or is nowhere dense then, for every definable set $X$, there is a family $ \ {x_t：\;在\ cal r中定义的t \ t \ in \ cal r和a in $ s \ subseteq a $ dimension $ 0 $，因此$ x = \ bigcup_ {t \ in s} x_t $。此外，在d-Minimal设置中，在先前表单的集合中有一个有限的分解，以便在$ \ bigCup_ {t \ in s}} x_t $中相对开放，每$ t \ in s $ x_t $中的每一个$ t \。
We prove that for an o-minimal expansion of the real additive group $\cal R$ and a set $P\subseteq \mathbb{R}$ of dimension $0$ such that $\langle\mathcal{R},P\rangle$ is sparse, has definable choice and every definable set has interior or is nowhere dense then, for every definable set $X$, there is a family $\{X_t:\; t\in A\}$ definable in \Cal R and a set $S\subseteq A$ of dimension $0$ such that $X=\bigcup_{t\in S}X_t$. Moreover, in the d-minimal setting, there is a finite decomposition of $X$ into sets of the previous form such that for every $t\in S$ $X_t$ is relatively open in $\bigcup_{t\in S}X_t$.
