Topics in o-minimal structures

该方案解决了o-极小结构模型理论中的问题，主要研究人员计划发展域的o-极小展开中可定义的集合的Borel-Moore同调。目标之一是研究可定义集合的特征循环。主要研究人员还将考虑代数变体中非阿基米德变形虫的模型理论方面。该建议属于数理逻辑的一个分支，称为模型理论。模型理论通过考虑结构中的一阶句子为真来研究数学结构，以及也满足所有一阶句子的交替结构族。(逻辑中的句子是由一小部分元素和结构组成的。“一阶”指的是句子中量词的数量，这是一种复杂性的衡量标准。)在许多情况下，这些替代结构说明了原始数学对象的一些属性。非标准分析就是一个很好的例子。这一建议的一部分是将非标准分析的思想扩展到解析几何范畴。

The proposal addresses problems in the model theory of o-minimal structures.The principal investigator plans to develop Borel-Moore homology for sets definable in o-minimal expansions of fields. One of the goals is to study characteristic cycles of definable sets. The principal investigator will also consider model theoretical aspects of non-archimedean amoebas of algebraic varieties.The proposal is in a branch of mathematical logic called model theory.Model theory studies mathematical structures by considering the first-order sentences true in those structures, and the family of alternate structures that also satisfy all of those first-order sentences. (Sentences in logic are built out of a small repertoire of elements and constructions."First-order" refers to the number of quantifiers in a sentence, a measure of complexity.) In many cases these alternative structures illuminate some properties of the original mathematical objects.A good example is the non-standard analysis. A part of this proposal is an extension on ideas of non-standard analysis to analytic-geometric categories.