论文标题
局部O最小结构和维度的前几何
Pregeometry over locally o-minimal structure and dimension
论文作者
论文摘要
我们为确定完成本地O-Minimal结构$ \ MATHCAL M $定义了离散的封闭操作。 $ \ MATHCAL M $和离散闭合操作的一对基础集形成了预制术。我们使用此事实定义了一组参数的可定义集的等级。可确定的集合$ x $的尺寸等于定义集合$ x $的公式的一组参数的排名。结构$ \ Mathcal m $同时是一阶拓扑结构。一阶拓扑结构$ \ Mathcal M $在一阶拓扑结构中可定义的设置的尺寸等级也与其尺寸相吻合。
We define a discrete closure operation for definably complete locally o-minimal structures $\mathcal M$. The pair of the underlying set of $\mathcal M$ and the discrete closure operation forms a pregeometry. We define the rank of a definable set over a set of parameters using this fact. A definable set $X$ is of dimension equal to the rank of $X$ over the set of parameters of a formula defining the set $X$. The structure $\mathcal M$ is simultaneously a first-order topological structure. The dimension rank of a set definable in the first-order topological structure $\mathcal M$ also coincides with its dimension.
