Mathematical Sciences: Homogeneous Structures, Strongly Minimal Sets, Model Theoretic Algebra

组合技术主要是由西蒙弗雷泽大学的Alistair Lachlan开发的，在许多涉及同质结构的分类项目中被证明是有效的。研究者打算进一步发展这一套技术，以寻找不能以这种方式分析的新类型的结构。他将继续麻省理工学院的Ehud Hrushovski的研究，尝试构造新的具有代数风格的强极小集，或者证明它们不存在。模型代数中的另外两个问题也在他的议程上。这种类型的模型论代数是数学逻辑和经典代数结构研究的混合。它有自己的特色，但可以阐明在传统方法中对这种结构进行分类和分析时出现的困难。

Combinatorial techniques developed primarily by Alistair Lachlan of Simon Fraser University have proved to be effective in a number of classification projects involving homogeneous structures. The investigator intends to develop this set of techniques further in the search for new classes of structures which cannot be analyzed in this fashion. He will follow up progress by Ehud Hrushovski of M.I.T. by attempting to construct new strongly minimal sets with an algebraic flavor or to prove that they do not exist. Two other problems in model theoretic algebra are also on his agenda. Model theoretic algebra of this sort is a mixture of mathematical logic and the study of classical algebraic structures. It has a characteristic flavor of its own but can shed light on difficuties which have arisen in traditional approaches to the classification and analysis of such structures.