Pregeometry over locally o-minimal structures and dimension

IF 0.4 4区数学 Q4 LOGIC

Mathematical Logic Quarterly Pub Date : 2023-08-30 DOI:10.1002/malq.202200069

Masato Fujita

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引用次数: 0

Abstract

We define a discrete closure operator for definably complete locally o-minimal structures $M$ . The pair of the underlying set of $M$ and the discrete closure operator forms a pregeometry. We define the rank of a definable set over a set of parameters using this fact and call it $discl$ -dimension. A definable set X is of dimension equal to the $discl$ -dimension of X. The structure $M$ is simultaneously a first-order topological structure. The dimension rank of a set definable in the first-order topological structure $M$ also coincides with its dimension.

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局部零最小结构和维数的预几何

我们为可定义完备的局部0 -极小结构M $\mathcal {M}$定义了一个离散闭包算子。M $\mathcal {M}$的基础集合和离散闭包运算符的对构成一个预几何。我们使用这个事实来定义一个可定义集合在一组参数上的秩，并称之为discl $\operatorname{discl}$ -dimension。一个可定义集合X的维数等于X的discl $\operatorname{discl}$ -维数。结构M $\mathcal {M}$同时是一个一阶拓扑结构。在一阶拓扑结构M $\mathcal {M}$中可定义的集合的维数秩也与其维数重合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Logic Quarterly 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematical Logic Quarterly publishes original contributions on mathematical logic and foundations of mathematics and related areas, such as general logic, model theory, recursion theory, set theory, proof theory and constructive mathematics, algebraic logic, nonstandard models, and logical aspects of theoretical computer science.