Mathematical Sciences: Research in Model Theory: Strongly Minimal Fusions and Other Homogeneous-Universal Models

小行星9510377 霍兰德的研究是在模型理论，一个分支的数理逻辑。 近年来，许多模型理论家感兴趣的新结构被构造成具有维数概念的有限模型类的泛模型。 在这些新结构中，有通过Hrushovski引入的融合方法从现有结构构建的新强极小结构。 霍兰德已经开始从几何学的角度对任意融合进行全面、系统的研究。 由此获得的新视角使霍兰德能够在特定情况下产生一种比赫鲁绍夫斯基更简单、更透明的结构。 她打算充分推广的简化和继续系统的研究融合都从几何的角度来看，看看有什么新的信息提供分类的几何形状所产生的强烈最小的结构，并从模型理论的角度来看，看看是否变化的强烈最小建设可能提供进一步的例子模型理论的兴趣。 与此同时，Holland打算努力建立一个统一的框架，在这个框架中，可以查看所有关于宇宙通用模型的新工作。 霍兰德打算利用规划期来完善她的研究项目，制定具体的、合理的方案，这些方案应该构成一个可信的NSF提案。 ***

9510377 Holland Holland's research is in model theory, a branch of mathematical logic. In recent years, many new structures of interest to model theorists have been constructed as homogeneous-universal models for classes of finite models with a notion of dimension. Among these new structures are the new strongly minimal structures built from existing ones by the method of fusion introduced by Hrushovski. Holland has begun a general, systematic study of arbitrary fusions from a geometric point of view. The new perspective gained therefrom enabled Holland to produce a simple, more transparent construction than that of Hrushovski in a particular case. She intends fully to generalize the simplification and to continue the systematic study of fusions both from a geometric point of view, to see what new information the provide on the classification of geometries that arise from strongly minimal structures, and from a model theoretic point of view, to see whether variations on the strongly minimal construction might provide further examples of model theoretic interest. In parallel, Holland intends to work toward a unified framework in which to view all of the new work on homogeneous-universal models. Holland intends to use the planning period to refine her research project, formulating the specific, plausible conjectures that should constitute a credible NSF proposal. ***